Born in South Africa, educated privately in the UK, settled with his wife and three children in the hipster heart of east London but speaking today from Rome, Johnny Flynn gets around. The actor-musician (half-brother to Jerome Flynn of the chart-topping acting-singing duo Robson and Jerome) is currently shooting a new TV version of Patricia Highsmith’s The Talented Mr Ripley. This one is being adapted and directed by Steven Zaillian, who wrote Schindler’s List and The Irishman, and stars Andrew Scott as the amoral antihero. Flynn, who has long forks of blond hair, as well as a scar in the shape of a question mark rising from the bridge of his nose (the result of a dog attack when he was three), plays Ripley’s idol-cum-quarry, Dickie Greenleaf.

It is the role for which Jude Law was Oscar-nominated in Anthony Minghella’s highly regarded 1999 film version. Daunting? “I won’t lie,” he grins when we talk via Zoom. “It’s definitely something I’m trying not to think about, which is an effort because I love that film.” This new spin, he says, is “quite beautiful and quite noir. It’s in the Fellini zone.”

The shoes he fills in the new wartime yarn Operation Mincemeat are even more illustrious than Jude Law’s loafers. The film concerns a real-life bit of second world war deception involving fake papers planted on a corpse to convince Hitler that the Allies were heading for Greece rather than Sicily. As a pre-James Bond Lt Cmdr Ian Fleming, Flynn is on the outskirts of the action, tapping away at his typewriter and amassing ideas for his future novels. Matthew Macfadyen – toadying Tom from Succession – is one of his fellow goodies. “Matthew is the sweetest, loveliest guy,” he says. “It’s quite a leap for me when I watch him as Tom. He’s really silly on set, loves giggling. We got told off a few times.”

Flynn goes wide-eyed as he considers his other co-stars: “Colin Firth. Simon Russell Beale. Oh, Kelly Macdonald! I had such a crush on her when I was growing up, from Trainspotting.” He wrinkles his brow. “Sorry, that’s kind of creepy.” Then a rethink: “I’m sure it’s OK, lots of people did who were a certain age when that film came out.” Now 38, he would have been 13 at the time: I think he’s in the clear.

Do he and Fleming have similar backgrounds? “I suppose so. The private school thing.” His memories of those years – first at the Pilgrims’ school in Winchester, then Bedales – are not entirely happy ones. “I was sent off to boarding school at the age of eight on a music scholarship, which was quite traumatic. Now my kids are around that age, it’s really poignant to me. It’s definitely something I think about.” He looks suddenly downcast.

Talk of Fleming leads to Bond. Would he care to throw his hat in the ring? “I don’t think I’m hard enough,” he says, practically retreating into his cosy brown pullover. “I literally don’t think I could hack the training. It’s potentially a poisoned chalice. It can be so defining, and I do like the freedom to do lots of different projects.”

In the past decade, this has included everything from the Netflix romcom Lovesick and a featherweight film of Jane Austen’s Emma (he was Mr Knightley) to the arthouse gem Clouds of Sils Maria, in which he shared a scene with Kristen Stewart, Juliette Binoche and Chloë Grace Moretz. If he has a brand, it’s rustic: he was an archaeologist in the Sutton Hoo drama The Dig and a charismatic poacher and possible serial killer in the Jersey-set thriller Beast, as well as popping up in the plangent BBC comedy Detectorists, for which he provided the lilting theme song. He has done a fine job of balancing acting with albums: his latest folk collection, Lost in the Cedar Wood, was co-written with the nature writer Robert Macfarlane, inspired by The Epic of Gilgamesh, and characterised, as Flynn himself is, by an earthy, rough-hewn beauty.

One blip last year was Bowie. Playing him in Stardust, set during the singer’s pre-Ziggy days, Flynn was in the firing line before so much as a frame of the film had been seen. Bowie’s son, Duncan Jones, threw shade at the movie on Twitter; fan fury and bad reviews followed. It was all very much not hunky dory.

“I didn’t go into it with my eyes closed,” he says now. “But I hoped people would take it for how it was intended. It was supposed to be this tiny independent film about a young artist, who just happened to be David Bowie, trying to find his voice, which I thought was a valid story to tell. It got judged for what it wasn’t rather than what it was. I was unhappy with some of the marketing around it. As the trailers were coming out, I could see mistakes being made and I felt sad that it wasn’t going to be seen. I’m still proud of it. These things are your babies. You put everything into them, and you want people to see the best in them.”

There are always other babies. On its way is The Outfit, a period crime drama with Mark Rylance, his stage co-star from plays including Jerusalem. Then there is The Score, a heist movie with Will Poulter in which the characters burst into song. Flynn’s own songs, to be precise. He’s thrilled with that one, he says, and generally happy to watch himself. “I’m always interested to see how it turns out. You think: ‘I was sure that bit was gonna be shit but it’s good.’ Or: ‘My hair looks better than I thought it would.’”

Operation Mincemeat is released 22 April.