Mr Johnny Flynn is used to dressing up, just not for himself. The actor-musician has been perfecting the dapper gent, donning some exceptional mutton chops and beige breeches, in four separate period dramas over the past two years. But a contemporary style shoot in a smart-casual coat? “I’ll be honest, it’s not the most natural fit for me,” he says, tugging his sandy hair in different directions. We’re on a train back to London from Whitstable, Kent, where the wind has made it look even wilder. “I don’t think about clothes very much. I wear black jeans and I have a number of shirts.” It’s whatever is lying around before the school run, where he often bumps into his Emma co-star Mr Bill Nighy. “Weirdly, his granddaughter is in the same class as my daughter at nursery,” says Mr Flynn, though the two actors also bonded over music. “He texts me weird things all the time about Bob Dylan.” His “real life”, as Mr Flynn calls it, at home in Hackney, with his wife Ms Beatrice Minns, a designer for the theatre company Punchdrunk, and their three children, sounds anything but starry. The 36-year-old might be about to release his biggest film yet – he plays top-hatted George Knightley in Ms Autumn de Wilde’s adaptation of Emma – but his outlook remains much the same as any well-meaning leftie who lives in east London. He no longer eats meat, cycles everywhere and adds that, as a family, they have tried to stopped flying.

Mr Flynn is the kind of guy whose idea of a lads’ holiday is retracing the steps of a pilgrim or poet with his nature-writer friend Mr Robert Macfarlane where, he explains, “you walk along ways that people have walked for hundreds of thousands of years” and can “immediately tap in to a sense of consciousness that’s existed through that time”. He is whimsical, but not in a pretentious thespian way, and he’d much rather discuss these adventures than how he’s emerged as one of the most interesting actors of recent years or how, thanks to his turn as Knightley, the “mansplaining” friend to the titular high-society meddler, he can now add dashing to his CV.

“Err, I dunno how dashing,” he cringes. “He’s a very flawed character. He’s overbearing. He preaches to her.” It’s true that Knightley keeps Ms Jane Austen’s narcissistic anti-heroine in check in a way that might now be interpreted as negging. “We can look at that through a modern lens, but, you know, Jane Austen was writing in 1815,” says Mr Flynn. Even though his leading man is “pretty irritating”, he has “some admirable qualities and his moral compass is quite true. I don’t think there were many men like that and maybe still aren’t that many.”

Mr Flynn plays Knightley quite straight, a slightly dishevelled bashfulness betraying his character’s stiff upper lip. He says it’s more challenging to play someone kind-hearted than somebody a bit more complex with “layers you can hide underneath”. Especially when it comes to talking about it in interviews. “It’s quite hard to be somebody who’s got to be quite naked, in a way,” he says. (As a side note, in his first scene in Emma, he does quite literally have his bum out.)

Mr Flynn’s roles so far feel very British, but not buttoned up, more undone and vulnerable than your average leading man. There’s something pleasing about the fact that he made his breakthrough in the Netflix show Lovesick as a character who must tell his one-night stands that he’s got chlamydia. Since then, Mr Flynn has swung broadly between mumbling, millennial will-they-won’t-they types and total psychopaths, both onscreen and onstage. After a spate of films in which he played variations of the former, he won critical acclaim for his roles as shadowy outsider Pascal in Mr Michael Pearce’s Beast and Mooney in Mr Martin McDonagh’s play Hangmen. Next, he’ll play Mr Ian Fleming in war drama Operation Mincemeat, and he’s taken on one of the most iconic Brits ever, Mr David Bowie, in the forthcoming biopic Stardust.

Mr Flynn is well-placed to play a young, folkie Mr Bowie. In the mid-2000s, Mr Flynn and his band The Sussex Wit were swept up in a London sound dubbed “nu-folk” and he would play alongside artists such as Ms Laura Marling and Mumford & Sons, some of whom he had met while studying music on a scholarship to Bedales. “The thing that drew me to the music when I first started was the pursuit of authenticity,” he says. His band and friends would wear checked shirts to be “reactionary to fedoras and winklepickers – the Libertines look”. But soon you couldn’t move for troubadours in tweed waistcoats on the pages of NME and, for Mr Flynn, things changed. “Then it became the whole mandolin-swinging folk aesthetic,” he says. “There were a lot of bands that we were touring with at the time that started getting really big and they were making consciously commercial choices.” He never saw himself as part of that circus, and his band parted ways with their label before they could make more than one album and find any commercial success themselves. Mr Flynn went back into acting.

It used to be that you couldn’t be a musician and a respected actor at the same time (remember when Mr Keanu Reeves was in Dogstar?) and so, at first, Mr Flynn tried to keep these two trajectories separate. “I wanted to be taken seriously,” he says. “I was really pleased when somebody said, ‘I didn’t know you were a musician,’ or ‘I didn't know you were an actor.’ And quite often people would say, ‘But you have to choose – which one do you want to be?’ and I loved doing them both.” To his surprise, however, the combination proved catnip to filmmakers. After Lovesick, he was a Brooklyn folk musician in Song One with Ms Anne Hathaway. He plays the violin as the young Mr Albert Einstein in the anthology TV series Einstein. “I don’t have much else in common with Einstein,” he says.

These days, Mr Flynn sees a synergy between the two art forms, especially when he’s acting in the theatre. “I learnt a lot about storytelling and relating to audiences through my time spent on stages with my band, trying to feel a sort of ephemeral energy and a sense of commonality,” he says. “Occasionally, on stage with a play, you can come close to that. I think about the push and the pull of the scene almost as a piece of music. I’m looking for the tune in the scene, where the drama becomes a melody.”

Acting, rather than music, is the Flynn family tradition. Mr Flynn’s father, Eric, played the title character in the 1970s TV series Ivanhoe and his older brother, Jerome, experienced floppy-haired fame in the 1990s as one half of the pop duo Robson & Jerome, although he’s probably better known today for playing Bronn in Game Of Thrones. “Theatre was a very romantic thing when I was a kid,” says Mr Flynn. He regularly watched his father’s dress rehearsals and hung out backstage. At school, he loved literature and history. “Reading Shakespeare in English classes at a desk wasn’t enough for me,” he says. “I wanted to be inside those stories, to investigate them.”

But, really, it’s more like he interrogates them. Whether he’s singing folk songs, acting in plays or retracing ancient pilgrimages, Mr Flynn is “fascinated” with what the past – even slightly fluffy period pieces with lots of high collars and ringlets – can tell us about the present. “I feel like there’s a responsibility to choose which stories are worth telling at this point in history,” he says. “There are lots of new stories being told, but I think it’s always interesting to look at stories we’ve looked at before. The age in which you exist tells that story in a new way.

“The moment that we’re in is not just this moment. It’s everything that has always been. I want to find out about myself through that sense of ancestry. Our natural interest in where we come from. Therein lies the key to life and understanding our passion for humanity.”

He says he took some convincing to play a young Mr Bowie in Stardust. The film, which has just wrapped and focuses on Mr Bowie’s first road trip to the US, where he finds Iggy Pop, Mr Andy Warhol and his alter-ego, Ziggy Stardust, is bound to draw scrutiny from the superfans. When Mr Flynn read the script, it seemed too daunting. “I just was like, ‘No. Nobody can do that. It’s just not worth going there. There’s too much risk. You’re setting yourself up for a fall.’” But a new director, Mr Gabriel Range, came onboard and wanted to tell a “more abstract, slightly darker story” about how inspiration can strike and change the course of someone’s life for ever.

The production was small and butted right up against filming for Emma. Mr Flynn had to quickly lose two-and-a-half stone and throw himself into filming. “It was pretty scary,” he says of playing such a celebrated icon, “but there wasn’t time to look back or hesitate. I feel a bit of pressure, but I’m not letting myself feel too much pressure. My face will never look like a replica of David’s face. I just don’t have that bone structure.” Stardust isn’t supposed to be a totally faithful retelling. Its scope is that of an arthouse film. “It’s not Rocketman,” says Mr Flynn, comparing it to biopics such as Control and Nowhere Boy. “A few years before that road trip, he sounded a bit lost in interviews,” he says. “It’s really interesting to look at an artist who doesn’t know where they’re going to go.”

Where will Mr Flynn go next? He might write some new music, as he is doing again, slowly. He might do something radical, such as his recent Radio 3 play, where he turned the story of poisoned Russian whistleblower Mr Sergei Magnitsky into a musical satire. Or he may go on another one of his pilgrimages, as long as it doesn’t require a long-haul flight. But first, he’s got to get off the train and take his son to a dance class. He turns down two separate offers of a taxi home and dashes off to catch the bus.

Emma is in cinemas on 14 February (UK) and 21 February (US)