It’s eerie being in a room with the Reeve siblings. All three are dead ringers for their father, Christopher. Matthew, 44, resembles Reeve as Clark Kent. Alexandra, 40, shares his angular beauty. The youngest, Will, 32, looks like him as Superman. They are almost as tall as their 6ft 4in father: Will is 6ft 3in, Alexandra 6ft and Matthew 6ft 2in. As for their jobs, Matthew makes films, Alexandra is a legislation lawyer based in Washington DC and Will is a TV sports journalist. Their father was a sport-obsessed actor-turned-director who campaigned to change the law on a number of fronts, most notably regarding disabled people.

“Strong genes!” Alexandra says, smiling at the other two. It’s not just that, I say. Your careers seem to reflect your father’s. Another smile. “It’s so strange,” Alexandra says. “We think about it all the time. We have split his passions between the three of us.”

It’s 20 years since Reeve died, 29 years since he broke his neck after being thrown from his horse, and 46 years since the first of his four Superman films came out. That film broke any number of box-office records and made Reeve a global star. Nobody mastered the screwball comedy of Superman and his bumbling alter ego reporter Clark Kent as convincingly as Reeve.

By the time he died, nine years after he was paralysed from the neck down, we realised that Reeve had a touch of Superman himself. But we didn’t know what a complex man he was. Now a new documentary, featuring his children and numerous household names, chronicles his life in all its intricate layers. The film has just had its British premiere at the London film festival, and we are meeting at a London hotel to chat about it. While Super/Man: The Christopher Reeve Story documents a unique individual, it also provides lessons for all of us. To distil it to its essence, how do we cope when the shit really hits the fan?

Reeve was born in New York into a well-to-do American family that goes back to the Pilgrim Fathers on his maternal side. His paternal grandfather was chief executive of the Prudential life insurance company, his father Franklin a poet and professor of literature, and his mother Barbara a journalist. Reeve had a privileged, successful and troubled childhood. He appeared to have it all: he was handsome, academic, a gifted actor and musician, and a natural sportsman. Yet he felt he could never be good enough to satisfy his father. His parents divorced when he was four, both going on to remarry and have more children. The family became forked and knotted. He didn’t quite know how he fitted in, or with whom. Reeve promised himself that when he grew up he would stay with the mother of his children and not make excessive demands of his offspring.

Yet it turned out he had more of his father’s genes than he had hoped, for good and bad. He sailed through exams, did well at everything he put his mind to, and turned out to be just as competitive as Franklin. After a trip to France in his teens, he returned home fluent in French – he’d not spoken a word of English in his time there. He went to the elite Cornell university and was one of 20 candidates out of 2,000 to win a place to study drama at the even more elite Juilliard School. He and his best friend Robin Williams were the only students in their years selected for the Juilliard’s advanced course.

At the age of 23, he auditioned for A Matter of Gravity on Broadway starring Katharine Hepburn, and was cast as her grandson. At the same time, he was appearing on TV in the soap opera Love of Life. He was so exhausted and living off such a poor diet that he fainted before he got his first line out. But it didn’t matter – Hepburn had taken a shine to him.

He took his theatre extremely seriously, as did his peers and his father. When he told his actor friend William Hurt he had an audition to play Superman in a movie, Hurt warned Reeve against selling out. Not that there was any chance of him getting the part. A number of stars coveted the role, including Arnold Schwarzenegger and Neil Diamond, while Al Pacino, Sylvester Stallone and Dustin Hoffman were considered, and Robert Redford and Clint Eastwood turned it down. When he was cast – against all expectation – Franklin bought a bottle of champagne to celebrate with him. But he had misheard. He thought Reeve had got a part in the Bernard Shaw play Man and Superman.

Would Franklin really have preferred Reeve to get a part in a tiny production of Man and Superman to playing the lead role in a blockbuster movie? “Seems like it!” Matthew says. “If you think about it, he was a literature professor, so theatre was the way of connecting with his son. Theatre is high art, not mainstream, commercial film.”

“It was a very traditional style of hard parenting,” Alexandra says. “In the US we call it Waspy parenting.”

“Patrician!” says Matthew, who seems anything but.

At the height of his success, Reeve and his father stopped talking for a number of years.

By the time of Superman II, Reeve was one of the world’s biggest stars. He was also now a father. Reeve had a relationship with British modelling executive Gae Exton, then left her for Jane Seymour, only to return to Gae when he discovered she was pregnant with Matthew. He and Gae went on to have Alexandra three years later, and lived in Britain where the Superman films were made.

As a little boy, Matthew remembers it dawning on him that his father was special. “Kids would come up and they’d want to spend time with him and get his autograph, but we still had a pretty normal childhood. It wasn’t California. We lived in London and New York for a reason – to have slightly more of a traditional upbringing.” Did Reeve enjoy his fame? “I think he took pride in how people connected with him, and the role of Superman in particular. It was fun to have kids come up, and he felt an obligation to live up to the hope that the kids were putting on you.”

Despite Reeve’s resolution, he and Gae split up when Matthew was seven and Alexandra was three. And despite his determination not to ape his father’s parenting, he did. He expected the best from his children, whether it was schoolwork, table manners or sporting prowess. Alexandra says he didn’t treat children differently from adults, which was great in a way, not so good in others.

“For example, we’d be skiing, and he would see the ‘double black diamond’ run for expert skiers. For Dad, it doesn’t matter your age, you just do it.” How old was she? “About six.” That’s crazy, I say. She laughs. “His position was you could take it at a slower pace. He’d bomb down to the bottom and wait for you.”

Then there was tennis. “Whenever he played, he played hard – even against a child.” It never crossed his mind, she says, that he shouldn’t serve at full strength against her.

Was this his way of teaching you or because he didn’t distinguish between kids and adults? “I think he was just an intense dude!” Alexandra says. “He didn’t slow down!”

Will chips in: “He was just a type A personality. Very alpha.” Reeve was also a licensed pilot who flew solo twice across the Atlantic.

Who’s the most alpha of you three, I ask.

Will: “No offence, Matthew, but intellectually, it’s Alexandra.”

“If you had claimed that it was me, I would have challenged you,” Matthew says. “With Dad, you had to make an effort. He had low tolerance for low effort.”

There’s an incredible clip in the documentary of the 27-year-old Reeve calling out Marlon Brando (who was paid $3.5m for two weeks’ work on Superman) for phoning in his performance. It was brave, I say.

“He didn’t see that as brave,” Will says.

“That reveals his personality so well – it’s like you have to try,” Alexandra says. “It’s true of Marlon Brando, it’s true of your children, it’s true of yourself. He was endearingly earnest.”

There’s another telling moment in the film when the young Matthew tells Reeve he’s not so different from his own father. “He didn’t want to be like Franklin, but as much as he tried not to emulate him, he inadvertently did,” Matthew says today.

The children say that Reeve was different from Franklin in a crucial way: he showed them so much love. “While Dad felt that he could never do anything well enough for Franklin, we did not have that at all as kids,” Alexandra says. “So his way of connecting with us was intense, but he was also full of pride. He celebrated every single thing we did.”

In 1987, Reeve met Dana Morosini, a singer and actor. He adored her, but he was still terrified of committing. He went into therapy to talk about his fear of marriage, and eventually he proposed. They married in April 1992, when she was six months pregnant with Will. Both Dana and Gae come across in the film as heroic – warm, loving, patient, the supportive hand the kids needed as they braved the double black diamond.

Reeve was back living in the US now. His Superman stint finished after four movies. Even when he was making them, he would return every summer to appear at the local theatre in Williamstown, Massachusetts, where he had started as an apprentice and now had a holiday home. He was looking to play more serious parts, in theatre and cinema. Despite impressive performances in Merchant Ivory’s The Bostonians and The Remains of the Day, it wasn’t easy to get cast in the roles he was hoping for. Theatre was a little easier, and his choices were bold. But even here he met with limited success.

Did he think he had become stereotyped? “He knew it was hard to get some roles after Superman or for audiences to connect with him,” Alexandra says. “Jeff Daniels says the audience just wasn’t ready to see him in the play Fifth of July, where Jeff and Dad play gay lovers. Dad felt those limitations. He wanted to keep pushing himself creatively, but audiences wanted to see him in a particular role because they were used to seeing him as Superman.” However much it stymied him creatively, Alexandra says, Superman gave him a great platform.

In the 1980s, still a young man, he spent much of his time campaigning on industry-related issues such as arts funding, and broader subjects including human rights and the environment.

In 1987, Chile’s rightwing dictator, Augusto Pinochet, threatened to execute 77 actors. Reeve flew out to Santiago, led a protest march and helped save their lives. A cartoon ran in a newspaper showing Reeve carrying Pinochet by the collar with the caption: “Where will you take him, Superman?” Reeve was later awarded the Grand Cross of the Bernardo O’Higgins Order, the highest Chilean distinction for foreigners.

“The way I remember spending time with him in the 80s is him attached to his fax machine doing advocacy work,” Alexandra says.

Did he regard himself as political?

“Yes!” all three chorus, proudly.

“Somebody asked him once whether he would run for Congress, and he went: ‘Run for Congress? And lose my influence in Washington?’” Will says. “He knew that because he could straddle the world of activism, but also not fully be an animal of that world, his voice cut through.”

In 1995, he made his final film before the accident, Above Suspicion, in which he played a police officer paralysed after a shootout. A decade earlier, Reeve had learned to ride horses for an adaptation of Anna Karenina, and by now he was a serious equestrian competitor. On 27 May 1995, in the week after the premiere of Above Suspicion, he was competing in Culpeper, Virginia, when his horse threw him. He landed on his head, and broke his neck. The world was in shock. It wasn’t simply a superstar who had been paralysed – it was Superman.

The subsequent surgery was radical and could easily have killed him. “In the film, Will says he literally had his head re-attached to his body,” Alexandra says. “He’s scarred my children for life with that phrase!” And is it accurate? “I don’t know if the medical profession would use that phrase! They were upfront that it was 50-50 whether he would survive that surgery. I remember before the surgery going in to say our goodbyes because we knew he might not make it through.”

Matthew: “The way I remember it, it was like 50-50 that he would make it till tomorrow for a while. Like every day, regardless of the surgery.”

In the film, we hear audio of Reeve saying: “I ruined my life and everybody else’s. I won’t be able to ski, sail, throw a ball to Will. Won’t be able to make love to Dana. Maybe we should let me go.” Dana convinced him to continue living. In the audio, Reeve says: “And then she said the words that saved my life: ‘You’re still you. And I love you.’”

Were the children aware that initially he wanted to die? “No,” Alexandra says. Dana and Gae protected them from that. “It was just dawning on him how different life was going to be. Not just for him, but for all of us, is how he frames it.

“He would have been the first person to say he had moments when he felt bitter. It certainly wasn’t all sunshine and rainbows. Of course he had days when he got pissed off at the circumstances.”

Robin Williams also convinced him life was still worth living. Soon after the accident, Williams visited him in hospital disguised as a Russian proctologist, telling him he needed an internal examination to see if he was still in working order. When Williams finally revealed himself, Reeve realised he could still laugh.

Williams took his own life in 2014. In the film, Glenn Close talks about the exceptional friendship between the two men, saying: “I’m convinced that Robin Williams would still be alive if Christopher Reeve were, too.” The children say Williams played such an important part in their father’s life. “He showed what it is to be a friend and to show up for somebody,” Alexandra says. “And his ex-wife Marsha is still incredibly close to us today.”

Reeve not only survived, but thrived. He made his first public appearance after the accident at the 1996 Academy Awards – one of the most moving moments at any Oscars ceremony. He looked gorgeous in his tux, and the standing ovation went on for an eternity. It had been a huge effort getting him from New York to Los Angeles. When the applause finally died down, he joked: “What you probably don’t know is that I left New York last September and I just arrived here this morning.” He used the opportunity to talk about “the power of film to present painful but important issues to the public” and “put social issues ahead of box-office success”. He rarely wasted an opportunity to talk about what mattered to him.

He went on to write two memoirs, as well as campaign to raise benefits for people with long-term disabilities, and secure more funding for spinal cord injury research. He told the world that he would one day walk again, hopefully by his 50th birthday (something even he couldn’t manage). He acted in films, notably playing a paralysed man in a remake of Hitchcock’s Rear Window, and directed films for the first time: In the Gloaming, a movie about a son with Aids returning to the family home to die; and the documentary The Brooke Ellison Story, about a quadriplegic girl’s battle to get into college. Perhaps most impressive of all, he taught himself to breathe independently for up to 90 minutes without a ventilator.

Was he as competitive as he had been before the accident? “I would say driven rather than competitive,” Alexandra says. “There was an intense focus on pushing his body beyond what the doctors told him it was capable of doing.”

“He was now competitive with himself,” Matthew says. “If he breathed off the ventilator for 30 minutes on the Tuesday, on Wednesday it would have to be 31 minutes.”

Do the siblings think their father changed after the accident? Alexandra says the whole family changed: “One of the residing feelings in our household is extreme gratitude. We didn’t walk around saying ‘thank you’ all the time, but there was a newfound appreciation among all of us for the way you spend time together, finding joy in the small moments. And the way we spent time together dramatically changed, so rather than being out and being active, the way you connected was just sitting in his office chatting. Which teenager sits and talks to their parents for two hours at a stretch? And suddenly that’s the way we connected.”

Reeve now spent time watching the world from his wheelchair. Did he become wiser? “I don’t know if he was wiser,” Alexandra says, “but he certainly had more perspective. Knowing how fragile things can be. Knowing not to sweat the small stuff. Knowing to be grateful for things you normally take for granted. That was probably the biggest change because it makes you reassess your relationships. It makes you bury the stupid quibbles and reforge friendships.” Crucially, he and Franklin made up after the accident.

Will, who was just shy of three at the time of the accident, says he’s not sure if his memories of Reeve before that time are real or forged by photographs and stories he’s been told. Either way, he thinks of his father as a man of action. “Prior to the accident, he could never sit still. The accident forced him to literally sit still, but figuratively he still couldn’t. He continued to push himself in every way – to grow as a husband, father, contributor to society.”

Will possesses one item of his father’s that he’s particularly proud of. “It’s a cover of the Wall Street Journal from 1997. He was gifted a gold plaque version of it, and the cover says: ‘The Reeve effect.’ There’s a picture of him and a graph that just goes tttttrrrrrrruh.” He arrows his left hand up to the sky. “And that shows the awareness of, and money allocated to, spinal cord injury research after his accident. The fact that our dad became the face of a movement and had such a tangible impact on people’s lives as a result was deeply important to him as a lasting legacy, and that continues today. If our dad believed in something, he would put his face, name and voice to it, and effect change. And he did a great job of that.”

On 9 October 2004, Reeve attended a hockey match Will was playing in. He always loved to see his children play sports. Reeve was being treated for an infected ulcer that caused sepsis. That night he went into cardiac arrest after taking an antibiotic for the infection and fell into a coma. The next day he died. He was only 52 and, despite everything, seemed to have many good years ahead of him.

The children say it was Dana who got them through this period. By then, all three were living in the US. “Those early days, we had paparazzi outside the house,” Alexandra says. “It was a zoo.” She looks at the others. “D’you remember when they did a TV special and Dana took us into Dad’s bedroom and we all watched? It was a day or two after Dad passed away. Dana taught us how to go through it.”

Will was only 12. Matthew and Alexandra returned to their father’s home to help Dana look after him. However crushing their grief, they weren’t alone. Throughout the film, Dana emerges as the glue in the family – lovable, loyal and so solid.

She seemed as much of a mother to you as to Will, I say to Matthew and Alexandra.

“Absolutely,” they reply in unison.

“She came into my life when I was three,” Alexandra says. “I don’t remember a time in my life without Dana. So she was that figure from the very beginning for me.”

Tragedy hadn’t finished with the Reeve family. A year later, Dana was diagnosed with stage four lung cancer, and 18 months after Reeve passed away she also died. She was 44 and had never smoked. Even though we only see her in flashback in the film, she is every bit as much its star as Reeve. Her death hits us like a slap across the face.

In the film, Will says: “Despite the love and security that my siblings provided me, and my family provided me, and my adoptive family provides me, that was the moment, 6 March 2006 … I’ve been alone since then.” It’s heartbreaking.

When I mention it today, he stresses how important the love of his siblings, his adoptive family and his girlfriend has been. At times, Matthew and Alexandra watch him talk with a pride and concern bordering on the parental. I mention it to them. They laugh it off, but they know there’s some truth in it.

“Those shoes are too big for any person to claim to fill, but we are definitely proud older siblings,” Alexandra says.

“They fill a middle space between parents and siblings for me,” Will says.

I ask why they agreed to take part in the film, after not talking publicly about their father for so long. They say that the time seemed right – 20 years since his death – not so close to his life that it’s too painful, and not too far that he’s forgotten. But as much as anything, they say it’s lovely to have his life documented for their families. Matthew and Alexandra have two children each (Alexandra’s son is called Christopher), while Will has a long-term girlfriend.

It’s amazing how often the siblings finish each other’s sentences; how symbiotic they seem. You sense that the death of Reeve and Dana has made them even closer. It’s remarkable that you’re so balanced and functional after what you’ve all been through – it would screw up so many families, I say. “We’d been given the tools,” Alexandra says. “It didn’t make it easy, but we’d been taught from a young age how you navigate crises. You keep breathing, you hug your loved ones really close and you just put one foot in front of the other.”

She pauses, and looks at the others. “There’s this Pablo Neruda quote Dad used to have up on the wall: ‘From strong roots grow flourishing leaves.’ And we had very strong roots.”

Super/Man: The Christopher Reeve Story is in cinemas in the UK and Ireland from 1 November