Johnny Flynn: Here's Johnny

The next time Johnny Flynn steps on stage, you probably won't like him. He plays Jim, the main character in a new play, The Low Road, by Bruce Norris (the American playwright responsible for the hugely successful Clybourne Park), which grapples with the subject of Western capitalism through the medium of an epic tale set largely within 18th-century America. Jim is a young upstart from rough beginnings – with an aptitude for mathematics and an ability to diddle people out of cash – who takes self-serving individualism as his creed.

Norris has crafted a play that is blackly funny, "a ripping yarn, like a fantastic Barry Lyndon-esque moral tale", Flynn suggests. It uses a large cast of characters to explore indirectly the workings of our financial markets and an economic system that may be rotten at its core. As Flynn points out, economic theory is a rather tricky subject to stage: "If you were to do a play that was out-and-out about Wall Street or the banks here, it would be a massive turn-off for me, and most of the people that this is aimed at. What the play is saying is that the people who are normal and don't have the propensity to understand money are the people who are being completely shafted, because there are these psychopathic sharks who are deciding how things should be governed.

"It's a great story that encompasses all of those issues but in a fantastic narrative and in characters that have emotional resonance, rather than just a presentation of the facts, which can be boring," concludes Flynn. Dominic Cooke, the outgoing artistic director of the Royal Court, for whom The Low Road will be his last production, has already described it as "the most ambitious play I have ever worked on".

The Low Road certainly is ambitious; it's also abrasive, and angry. None of which are words you would really apply to Flynn. Mild-mannered and softly spoken, he is a somewhat unlikely star. Yet this English actor and musician, who turned 30 earlier this month, would appear to have the world at his feet: he pops up in many of our country's most exciting theatrical events: in the smash hit Jerusalem (starring Mark Rylance), and in last summer's Shakespeare double-bill at the Globe, Richard III and Twelfth Night, again with Rylance – and also with one Stephen Fry (who was "wonderful, he just completely went for the process"). He's slated to star in a film, Song One, about an archaeologist who falls for a rock star; Oscar-winner Anne Hathaway would play the former, Flynn the latter. Which is a neat bit of casting given that he also fronts a rather excellent band, Johnny Flynn & the Sussex Wit, who have recorded and toured with the likes of Laura Marling and Mumford & Sons, and who have a third studio album out later this year.

Sickening, isn't it? And if the talent wasn't enough, a quick Google search throws up very pretty pictures, too, a blond-haired, blue-eyed golden boy – looks which stood him in good stead not only for a role in forthcoming feature film Lotus Eaters, about rich, beautiful, ennui-ridden bright young things, but also for a modelling job with Toast.

In person, Flynn is a less glossy, more earthy, prospect. We talk during a hectic lunch-hour within a packed rehearsal schedule (he apologises for eating a salad while we chat, and is mortified when a bit of potato flies off the fork and on to the floor). He's gently dishevelled; the odd button undone on his plaid flannel shirt, the shock of blond hair a bit messy (though not artfully so). His manner is gentle, too; meandering answers appear vague at first, but it's soon apparent this is thoughtfulness, rather than wariness.

That he has ended up performing is no surprise. His father, Eric Flynn, was also an actor (with the RSC, many West End musicals, and in TV shows including Ivanhoe and Doctor Who) – although he died in 2002, before seeing much of his son's success. One of Flynn's half-brothers is Jerome Flynn (of Soldier Soldier and Robson & Jerome fame), while his sister Lillie Flynn is also an actor – recently appearing in the musical Wicked – who has sung with her big brother in the Sussex Wit.

They grew up in the country: the Wiltshire/Hampshire border, moving to Pembrokeshire in Wales as teenagers. This meant that, when Flynn first encountered Jez Butterworth's play Jerusalem, it felt very familiar. He joined the cast only for the final London run in 2011, but had caught its original incarnation at the Royal Court as a punter. "I bought one of the last tickets in the top, top circle, sat in the back row, and it was still the best play I'd ever seen," he says. His other reaction: "Well, that was weird – that's my childhood."

Jerusalem is set on St George's Day, at a caravan belonging to the eccentric Rooster Byron (played by Rylance), who attracts local teenagers and small-town misfits for mad parties in the woods. It also has a deep seam of folk-lore running through it, and is as much a hymn to Olde England as to contemporary England. Flynn was captivated by its hilarious, devastatingly accurate portrayal of a close rural community, something that defines our country yet is rarely portrayed on stage.

Flynn grew up in a village near Andover, which is even mentioned in the play. "Me and my friends used to go on our bikes up this lane to where the travellers were, we'd go and hang out with them – well, we weren't really allowed to – so [Jerusalem] was very familiar landscape. And there have been people in my life [like Byron], sort of deviant, spiritual masters – I know that they're flawed but I've embraced them because I've realised there's something I can learn from them."

The play was a hit in America, too, and by the end of the second London run, newspapers were reporting on Jerusalem fever, people queuing outside for days – in k freezing-cold January, no less – to get tickets. How did it feel to be part of that? "Everyone was just really grateful, and Mark was a good leader of that – he'd make really amazing speeches to the people who had queued through two nights in the cold," he says. "We'd go out and give them whisky and cake."

Jerusalem didn't just jog memories of previous masters, it introduced Flynn to a new, deeply important, one: Mark Rylance. "I really love him. He became kind of a mentor for me – without him imposing that on me at all! Certainly, he doesn't want to be above anybody, his whole thing is about being one of the players."

If that sounds gushing, it isn't at all. Flynn speaks with a quiet, contained, un-thespy manner – although, when discussing sharing a dressing-room with Rylance, he does add that "everything he says you just want to keep" and clutches his hand to his heart. "He's a very wise and humble and gracious person… But he's naughty as well! I think that's why he played the Rooster Byron character so well, because the positive sides of Rooster – the mischievousness – that's really Mark through and through."

In Jerusalem, and in Richard Bean's 2011 play The Heretic (also at the Royal Court), and in the plays he did with Ed Hall's all-male troupe Propeller, Flynn has had the chance to perform songs. Yet even so, he is keen to keep acting and music separate: "I take them both seriously – I don't particularly want to be an 'actor-musician'. I want to play the great challenging parts, to be right for the part, rather than just, 'Oh, he can play the fiddle.'"

He sings in Lotus Eaters, too – the black-and-white debut film of director Alexandra McGuinness (daughter of music manager Paul McGuinness). It did the film festival rounds in 2011, but is getting a limited release, finally, this month. Although generally unimpressed, a review in The Hollywood Reporter praised Flynn's "incredible charisma and presence" as a posh heroin addict, adding that "his unplugged performance provides the movie's one break-out moment".

hen there's Song One, which sounds like another hipper-than-thou project, even with a mega-star like Hathaway on board. It's being developed by filmmaker Kate Barker-Froyland with musicians Jenny Lewis and Johnathan Rice (of the bands Rilo Kiley and Jenny and Johnny). Will he have any musical input? Flynn starts to laugh, a little unsure of the etiquette here: "I don't know what I should say because it's not 100 per cent… there hasn't been a proper offer yet. I just met [Lewis], and have been talking to her about the music for the film… [But] I'm happy to treat it as an acting job."

He's keener to talk about his own new album. His primary relationship in the band is with bass player Adam Beach, his best friend and long-time collaborator. "He is a genius. He's one of those people who's all about music, he doesn't want money or anything," says Flynn, adding rather sweetly, "I feel like I need to look after him."

They've been recording, slowly, for two years – a very different process to the workmanlike five weeks in a studio of previous albums. They've ditched the crew, too, doing the production themselves. "I called it 'demoing with intent'. My thing about demos is that you usually prefer them to the finished thing." So they did their demos in "a really nice studio, recording it properly". And those fresh, first drafts have become the finished album, out later this year.

Flynn's previous records have been loosely branded folk-pop or nu-folk, thanks to the use of fiddle, mandolin and banjo, and poetic lyrics featuring pastoral references to harvests, orchards and, erm, cow-tipping expeditions. The second, 2010's Been Listening, rode the folk-revival wave; what did he make of that? Was it annoying, being told you were part of a "scene"? "It was really annoying," he deadpans.

This is followed immediately by a burst of laughter, but he adds, with a degree of discomfort: "I never really wanted to be put in the same breath as… anyone else. Not because I didn't like what they did but… There's always been pockets of people who just know each other. I guess it is a movement – but the movement is about collectives in small communities, and I've been part of lots of those collectives…" And it just so happens that a few people in one of those collectives – step forward Mumford & Sons – have "conquered the world".

Not that he's aiming at similar domination. "I don't have the desire to do that. My only incentive is to write music that changes me, where the process of making it is a discovery, and is true in some way, at that moment." More romantic idealism than shrewd business plan.

Flynn adds that he can't even remember writing many of the songs this time round – "Normally I have loads of notebooks, but this just kind of happened. You feel like you've found a song, whole." Perhaps the writing process seems a little hazy because of another big arrival: Flynn and his wife Bea, who live in Hackney in east London, had their first son, Gabriel, nearly two years ago.

It must, I imagine, be a challenge to have a young kid and record albums, rehearse plays, shoot movies… "It has thrown everything into perspective. I just rush home now, whenever I can, to make the space. My wife works full-time as well, yet we get a lot of each other. It's a mystery – we're figuring it out!"

Fatherhood has found its way on to the new record, too – there's a lullaby about him and his son hanging out together. Flynn adds, in gently hippyish musing mode, "He's teaching me a lot. I feel like he's some kind of sentient being who is teaching me stuff from a higher plane, it's a wonderful thing. You don't know what [having a child is] going to be like until you're there. It's overwhelming. It's great."

An angelic baby son and Mark Rylance as your teachers? No wonder Johnny Flynn's star is shining so bright.

'The Low Road' is at the Royal Court, London SW1 ( royalcourttheatre.com) to 11 May. 'Lotus Eaters' premieres at Curzon Soho, London W1 ( curzoncinemas.com), on 28 March