With his father, the legendary director John Huston, it was that gravelly voice that you noticed first. With his sister, Anjelica Huston, it is her magnificent nose. And with his nephew, actor Jack Huston, it’s the moustache. But with actor-director Danny Huston, it is, unarguably, the eyebrows: those great looping Ls that waggle away as you chat with him, as if they were having their own separate conversation with you. People often talk about his resemblance to his father, but, I tell him, the celebrity he always looked most like to me is Jack Nicholson, thanks to those brows.

“Yes, Jack defined these eyebrows before I was able to grow into mine,” he grins, bearish in size and wolfish in smile. Isn’t it a little weird for his sister Anjelica that her baby brother looks so much like her ex-boyfriend? “Hmmm, I know what you mean. Well, I think that only enabled her to have greater affection towards both of us – ha!”

Those distinctive features have also helped to make him one of the most ubiquitous and enjoyable character actors to have emerged in the past two decades. He deployed them to superb effect in his breakthrough performance, in one of my favourite films of the early 2000s, Ivans xtc, a modern retelling of The Death of Ivan Ilyich, directed by Bernard Rose, in which Huston played a drug-addicted Hollywood agent who feels death’s cold breath on his neck. Imagine Robert Altman’s The Player, but more pitiless and with more heart, simultaneously.

It was Huston’s first major acting role, having intended to be a full-time director, but he was so extraordinary in it that his little lark turned into an accidental career. Martin Scorsese cast him as airline magnate Jack Frye in The Aviator, and he looked more at home in Hollywood’s golden era than Leonardo DiCaprio. As evil General Ludendorff in Wonder Woman, those eyebrows made him look ferocious and pleasingly cartoonish, and as moneyman Jamie Laird in Succession, he was lugubrious and calculating.

“When I was making [the 2005 film written by Nick Cave] The Proposition, the director John Hillcoat took me aside at one point and was having trouble saying what he wanted, and I said, ‘What? Just tell me!’ And he said, ‘When you turn around, can you to keep that eyebrow down?’” he says, and laughs again.

Huston, 58, is talking to me by video chat from his home in the Hollywood hills. The Hollywood sign is behind his house “but you really have to crane around at a right angle to see it. It’s not in your face,” he says. Hanging behind him is a drawing of a racehorse given to him by his nephew Jack, who recently played Bobby Kennedy in The Irishman.

“It’s nice, huh? Yeah, Jack’s doing great in the family business,” Huston says. He also has a home in Berkshire, which he describes as “a family home”, where his mother, the actor Zoë Sallis, is staying, and where he and his partner, the English actor Rosie Fellner, and their two-year -old daughter, Luna, will spend the summer. (He also has an 18-year-old daughter, Stella, from an earlier relationship.)

Before the interview, I promised myself I wouldn’t ask Huston too much about his fascinating family, a proper Hollywood dynasty with roots as deep as the Barrymores, going back to his grandfather, the Oscar-winning actor, Walter Huston. But his relatives prove to be unavoidable because he is surrounded by them, even if they’re not in your face and you have to crane a little to see them. “My relationship with film began with lacing film into old projectors, anxious maybe the film would rip, then the beam of light through some [of my father’s] cigar smoke on the wall and then,” he smiles, holding up his hands in a “ta da” pose, “there’s my grandfather.”

We’re talking today about Huston’s latest film, The Last Photograph, in which he stars, and it also marks his return to directing after an almost 20-year break.

“I wanted to get back in the saddle and the reason I cast myself was I knew I was available,” he says. Adapted by Simon Astaire from his novel of the same name, the film opens with a morose bookseller, Tom (Huston), realising that his bag has been stolen from his shop, and in the bag is a hugely important photograph. We then learn in flashbacks why that photo was so significant to him, and the cause of his unhappiness. Huston’s eyebrows do sterling work in helping to delineate the timelines: in the scenes from the 1980s before the tragedy, they dance about happily; in the present, they hover hopelessly.

It’s not really a spoiler to say that Huston’s character suffered a terrible bereavement, and it involved the Pan Am 103 flight, which exploded over Lockerbie in 1988. Huston is excellent at conveying the heaviness of grief and the scene in which he finally realises that his loved one has been killed is unbearably poignant.

“The closed nature of the character, the psychological difficulty he’s had trying to make sense of the tragedy, even all those years later – I thought that was interesting. Time heals all wounds? I don’t think so. It doesn’t,” he says.

I ask if there were losses in his past that he drew on for the role, thinking he might mention friends who died, or Katie Jane Evans, the mother of his older daughter, who killed herself during their divorce. But instead, he goes back to his family.

“Yes, absolutely. The people I loved who are no longer here, the small things that make them relive but also break my heart. It’s the 80th anniversary of The Maltese Falcon [which his father directed] and when I see my grandfather in small parts, like in The Treasure of the Sierra Madre, he comes alive again. We all have last photographs, things that are closed off and tucked away,” he says. Among those tucked away things are elements of his personal life: like Nicholson, Huston has a naughty glint in his eye and when I ask about some of the tabloid stories he’s appeared in he says they are too complicated to discuss. So we return to the comparatively safer ground of his family.

Was going into film-directing a way of staying close to his father? “Yes, absolutely. I grew up on his film sets so I’ve always been comfortable on sets. Telling stories, that’s the family thing,” he says.

Huston was born in Rome in 1962, after his parents had an affair when his father was directing and his mother was starring “in a film based on a rather well-known book called the Bible”. As well as directing The Bible, John Huston played Noah and the voice of God.

Therapists would have a lot of fun with that, I say.

“Exactly! And my mother was playing Hagar [Abraham’s second wife], and she had a child dying from thirst in the desert, and the child wasn’t me. That’s where the therapy starts. I had a lot of difficulty separating truth from fiction with those characters,” he says.

Huston didn’t have “a Hollywood upbringing” because his father was living in Ireland, having turned his heel on the US in disgust during the House Committee on Un-American Activities investigations, which resulted in the blacklisting of many of his friends. So Huston was raised in Ireland and England, and still has US and UK citizenship. But given that John was married to Enrica Soma, the mother of Anjelica, Allegra and Tony Huston, when Danny was conceived, and remained so until Soma’s death in a car accident in 1969, I tell him I assumed that his father wasn’t around much when he was growing up.

“Oh no, he was very involved in my childhood. He was like a pirate that would return from faraway countries, bearing gifts. I was lucky enough to visit him on film sets, like up in the Atlas mountains when he was making The Man Who Would Be King, and there was Connery and Caine and Christopher Plummer. For a young boy, it felt like the absolute adventure,” he says.

I ask if it was ever awkward between him and Anjelica, given that their father was married to her mother when he was conceived.

“Ummm no, I don’t think it ever was. We hit it off right from the start, and she was always very caring, my angel, my big sister. And she was really cool – she knew the Rolling Stones! She would take me out to various scenes that were cool for a kid to experience,” he says with, I imagine, some understatement.

It was his dad who gave him his first directing job back in 1984. “I would go around the world with my father and I would make his drinks for him, the flavour depending on the place. So he was shooting Under the Volcano with Albert Finney in Mexico and for some reason he was drinking Cuba libres. So I would make his rum and Cokes and normally he would complain and say, “No no, the Coke is only there to colour it!’ But my father was having trouble with the title sequence, it was too slow, and I’d been to film school, so I said, ‘You could do this…’ And he said, ‘You do it!’ And it made the cut,” he says, the filial pride still in his face.

Still, did he never think, “Maybe I shouldn’t do the job for which my father got 13 Oscar nominations and two wins?”

“Oh very much so. I rebelled for a while. Drawing was what I was really into – you don’t need anyone else’s money or permission to do that, you just pick up a pencil. But then I realised what the art scene was, and there might be even more grossness there [than in film],” he says, and clearly the only career options that exist are artist or film director.

His family sweetly encouraged his entry into the family business. His sister starred in his first directing job, Mr North, and his father initially agreed to appear in it too, but he then fell ill with the emphysema that would ultimately claim his life in 1987. So instead, John asked “an old friend” to appear in his young son’s film, and that friend just happened to be Robert Mitchum. Since then, Huston’s sister has regularly appeared alongside him in films and, in Ivans xtc, Anjelica’s now late husband, the sculptor Robert Graham, played his father. There is no doubt that Huston grew up with enormous privileges, but the cross-Huston pollination in films reads to me more like genuine familial closeness than simple backslapping and nepotism.

“Yes, I am very close to my sister, and my father had real generosity and bravado, and he was very generous with me,” he says.

Was he reminded of his father when he worked with Brian Cox while they were making Succession together? Certainly Cox has bravado to spare.

“Yeah, he does, he does. I have a crush on Brian – I absolutely adore the man. The two of us would talk about old films on the set and he has this wonderful glee about him, this force of nature, and my father was all of those things.”

Never mind his father’s achievements, if I were Huston, I would envy the times in which he lived, when Hollywood figures really were forces of nature, not PR-controlled automatons, and when a man could romance socialites and it wouldn’t live on the internet for ever. I expected Huston to be annoyed by all the interest in his family, given that he, unlike so many other Hollywood progeny, has genuinely made a successful career for himself. But he seems to have more fascination with them than anyone. When we talk about what he’s doing next, he says he’s developing an adaptation of something by Hemingway, who was close friends with his father. In fact, his father had tried to adapt Hemingway’s novel Across the River and Into the Trees, and now that an adaptation of that book is finally in production, Huston himself will appear in it.

“I remember my father writing the screenplay, so it just made cosmic sense to be in it,” he says. And this time when he smiles again he looks less like a wolf and more like a son who simply loved his father.

• The Last Photograph is released digitally on 26 April.