The sun is out and so is Baz Luhrmann. We meet at the Piccadilly theatre, home to the new stage version of his splendidly camp comedy-musical Strictly Ballroom, but he insists on heading to a nearby park. A publicist and assistant march ahead of us, clearing a path and stopping the London traffic. “This is the best idea ever!” Luhrmann announces, offering his bare arms to the sun. We find a bench near rows of gaily coloured tulips that are in danger of being upstaged by the 55-year-old, with his silver quiff and sunglasses, short-sleeved lemon-coloured floral shirt, pinstriped trousers and gleaming white trainers (no socks).

Luhrmann has the air of a princeling about him, but it would be churlish to say he hasn’t earned it. Strictly Ballroom, his film debut, arrived in 1992 in a haze of sequins, satin and hairspray, although it looks positively austere now, compared to the director’s following films. Romeo + Juliet, which reimagined Shakespeare for the ecstasy generation, remains the daring pinnacle of his career. He calls it “the most romantic film-making experience I’ve ever had. Someone should make a film about us making that film. Can you imagine? Leo DiCaprio was 19, we’re all living in Mexico, there are helicopters and explosions and we’re doing iambic pentameter! I’ve never waited for permission to do anything. People just say, ‘He’s a bit crazy, but let’s give it a go.’”

Moulin Rouge was next, a hectic musical edited at stroboscopic speed with the sounds of U2, Elton John and Nirvana ringing out across fin-de-siècle Paris. After Australia, a self-consciously old-fashioned epic, he was back to his breakneck self with a bells-and-whistles spin on The Great Gatsby, complete with Jay Z-produced soundtrack. Purists were aghast, though the film made $354m worldwide.

But Luhrmann’s 1970s-set origins-of-hip-hop series The Get Down was cancelled last year by Netflix, after a single season that was rumoured to have cost $190m. The production was subject to so many interruptions that it reportedly became known as The Shut Down. When he couldn’t commit to a second series due to film-making obligations, Netflix pulled the plug. “I was just gonna be the uncle to it,” he says. “What they didn’t know was how to use music in storytelling, so I went in deep, as I always do.

“I’m the least likely person who should’ve done the birth of hip-hop, but I’m also the least likely one to film America’s greatest novel or turn the Moulin Rouge into a musical. I’m from a tiny country town. I’m from the planet Audience. I’m far away, gazing at everything, and it all looks amazing to me. Still!”

Luhrmann is weighing up which of two projects – one a “Chinese-y” western, the other an Elvis movie – to begin first. At any particular time, he might be found managing the opening of a luxury mall, launching his own vodka or orchestrating the Christmas window display at Barney’s in New York. “I’ve always been spread too thin,” he says.

Strictly Ballroom, though, is where it all began. It started out as a 20-minute devised theatre piece, staged when Lurhmann was studying at the National Institute of Dramatic Art in Sydney. The reaction was ecstatic. He had already taken acting jobs to fund his first theatre company – he played a pig-seller-turned-hearse-driver in the Aussie daytime soap A Country Practice – but the response to Strictly Ballroom persuaded him to give that up. “I knew for good or bad I would be making shows for the rest of my life.”

There were several iterations of Strictly Ballroom, including a Brechtian one, punctuated by speeches from Reagan and Thatcher. “What I was trying to do, in my ham-fisted way, was connect the idea that, whether it’s ballroom dancing or politics, there will always be some carnival barker saying there’s only one way to cha-cha-cha.”

When he filmed Strictly Ballroom, Luhrmann was already a theatre and opera wunderkind, with a rulebook-shredding La Bohème (later revived on Broadway) to his name. The current stage incarnation, which debuted in Sydney three years ago, lifts everything from the movie, including the costumes designed by Luhrmann’s wife, multiple Oscar-winner Catherine Martin, and the ugly duckling plot, in which spotty misfit Fran pairs off with rebellious hoofer Scott to overturn the staid conventions of ballroom dancing upheld by fearsome federation president Barry Fife.

New trimmings include a rollerskating MC, winningly played by Will Young in a spangly catsuit, and an eclectic, Moulin Rouge-style soundtrack resulting in such did-I-hear-that-right? moments as a medley incorporating Public Enemy’s Fight the Power and REM’s It’s the End of the World As We Know It (And I Feel Fine). Luhrmann is energised by the oddball. “People don’t come to the theatre to watch you be careful.”

That’s the whole point of the show, as suggested by its signature line: “A life lived in fear is a life half-lived.” (Luhrmann admits he borrowed it from the late-1970s martial arts show Monkey.) The similarities between him and Scott are clear – like his protagonist, Luhrmann was a ballroom dancer from the age of six, while the establishment’s objections to Scott’s “flashy, crowd-pleasing steps” now sound like reviews for any one of the director’s films.

Watching the production a few days ago, though, he felt more like Fran than Scott. “The ugly duckling myth isn’t about transformation. This is a cygnet who by accident finds herself among ducklings, so it’s about self-revelation. In that regard, I think I’m only getting started.”

Luhrmann was raised in the seven-house town of Herons Creek, 225 miles north of Sydney, where his family owned a farm and a gas station. His father was a navy man who had fought in Vietnam, his mother a dance teacher. Parenting was an unconventional mixture of the artistic and the military: “Ballroom dancing and commando training,” as he puts it. “Whether we were working or breeding fish or waterskiing or scuba diving, it was wall-to-wall activity. Relentless.”

There have been plenty of Barry Fifes in his own life, he says. “They’re everywhere. There’s a few winks to a current one in the show.” Barry, who harbours political aspirations, sported a garish flap of orange hair as far back as the original film. “Ahead of the curve, right?” Luhrmann laughs. He thinks that’s true of all his work.

“My films are usually like baby seals, and everyone is trying to club them to death. But I was always making things for the future. I didn’t want to be hip and groovy for a brief moment. I was hoping it would move through time and geography.” He feels an affinity with his friend and compatriot Kylie Minogue, whom he cast in Moulin Rouge as the Green Fairy. “People were so vicious to Kylie. They called her talentless. But she has prevailed.”

As has Luhrmann. His influence is everywhere in popular culture. To take one small example, there’s the word “Strictly”, which in the early 2000s was tacked on to a reboot of the late-night dancing contest Come Dancing. “A lady at the BBC loved the film and tried to get a TV version made that didn’t happen,” says Luhrmann, who has appeared as a judge on the US version, Dancing With the Stars. “I was terrible. My whole life is about helping artists be better, not saying, ‘You suck.’”

He and Martin – whom he calls CM – live with their two children, aged 12 and 14. Whether at their homes in New York or Sydney, husband and wife inhabit different floors and sleep separately, convening at the weekend for a hotel date night. Do they still have sex? “Yeah, we do. And you know what? She rocks out. She’s a bit of a wolf. She always dresses up in strange costumes.”

And him? “Look, it’s never gonna be like when you were 20. I’m not saying it’s boring, but it becomes part of the ceremony: the intimacy, the talk afterwards. Our relationship is full of acceptance. She knew who I was going in, and I knew who she was. Without going into details, we’ve lived a pretty boho life. There’s nothing about either of us that the other one doesn’t know. We have our way, and that works for us.”

They met in the late 1980s and were married in 1997. Martin, though, didn’t know him when he was plain Mark Anthony Luhrmann. Where did the Baz come from? “I had this crazy curly hair, this big ’fro, and at school there were all these boys in their uniforms who used to beat the shit out of me. They called me Basil Brush and the name stuck. At some point I changed it by deed poll.”

So he reclaimed the insult, in other words, just as gay people did with the word queer? “I didn’t think about it at the time, but that’s exactly what happened. ‘I’m Baz! And you’ll be hearing from me!’”

• Strictly Ballroom the Musical is at the Piccadilly theatre, London. Box office: 0844-871 7630.