Daniel Mays is going straight...straight to a camp comedy, that is

After a decade playing rogues, gangsters and reprobates, this son of an Essex sparkie is emerging as 2013’s brightest star. Next up is a ‘full-on, camp comedy’ starring role at the Donmar Warehouse. Don’t joke...

In a new, four-hander play called Hero, the actor is Jamie, a primary-school teacher. He's not gay, but it seems that some of his seven-year-old charges think he is. His colleague Danny (played by Liam Garrigan), however, is gay – yet none of the kids know it. Both teachers are trying to have babies: Jamie, via IVF, with his wife; Danny, via adoption, with his husband.

Set in the kitchens of each of the couples' flats, the drama ricochets around the Royal Court's top-floor stage, the audience arrayed up both lengths of the intimate theatre. For Jamie, abusive notes pushed through his letterbox quickly escalate to gay-bashing. Now he's burst into the likeable, inspirational, hero-like Danny's home, bleeding profusely, gesticulating wildly – and quickly digging himself into a hole of his own homophobic making.

"The character you've just seen here is deeply, deeply unsympathetic," says Mays when we meet in the Royal Court's bustling basement bar post his matinée performance, "to the point where people might shy away from him, or his homophobia, or whatever it is. But I'm not scared of showing the ugly side of a character. If that's what they are, that's what they are. You can't have an ego doing this job; you can't have anything to do with vanity."

He takes a glug of his Coke. Mere minutes after coming off stage, the 34-year-old is still rippling with the electricity he brought to the wired, confused Jamie. He quizzes me about Hero. Did I think Jamie was himself gay? Did I like him? Did I follow the second act's non-linear chronology? Broadly, did the play and the performances work? This Essex-born son of an electrician might be Rada-educated, but he's certainly no luvvie seeking approbation or flaunting floridity. He's just keen to know if he and his cast-mates have done their jobs properly.

"It's about investigating why the character behaves in that way," Mays continues. "It's about doing the homework. So in that way you just humanise Jamie as best you can. Because there's many different levels to that character. He is funny and awkward, and there's a sensitivity to him at times as well. But in the end it's that darkness that comes out."

Mays is good at darkness. He was roguish – and ultimately deeply selfish – as Ronnie Biggs in ITV's big-budget autumn 2012 drama, Mrs Biggs. A year ago he was raging as a convicted killer protesting his innocence in the BBC's Public Enemies alongside Anna Friel. In Channel 4's 2009 Red Riding adaptation of David Peace's novels he was utterly compelling as the youth with learning difficulties accused of a horrific series of murders. As the guy behind the counter in the Royal Court's bookshop had said to him after seeing Hero: "Great work – a typical Daniel Mays part."

As he recounts the latter, Mays looks pained. He feels it's faint praise. Is that him, a young actor on the rise, painted into a corner already? But then he admits he knows where it comes from, his ability to shine a light into characters' murkier corners. It dates back to the first proper film he did after leaving London's Royal Academy of Dramatic Art (discounting a blink-and-you'll-miss-him micro-part in the big-budget flop Pearl Harbor). After a typically exacting audition process, Mike Leigh cast Mays in All or Nothing (2002). In quick succession there followed another collaboration with the infamously rigorous director, Vera Drake (2004).

"Without a shadow of a doubt, doing those two films with Mike early on has made me the actor I am," states Mays. "He's infused that thing of leaving no stone unturned when you're in the pursuit of playing a truthful character. It's a method that works. And I do try to apply it to other stuff, but it is a technique that is exclusive to him.

"I got known for doing a lot of troubled parts, like you've just seen, angry young men or whatever," he shrugs, stretching his 6ft 2in frame in his chair like he stretches the Estuary vowels in his mouth. "And one thing leads to another. But it's about when you get to that point where you do get a bit of a name, to then try to be bold and take a character that'll push you in a different direction."

In 2013, Daniel Mays is getting his wish. Hero finished its Royal Court run just before Christmas. After little more than a week off at his East Finchley home with girlfriend Lou (a make-up artist), seven-year-old son Mylo and two-month-old daughter Dixie, last week Mays was already treading the boards again. He's begun rehearsals for his next London play, the Donmar Warehouse's production of Arthur Wing Pinero's 1898 comedy Trelawny of the Wells. It's being directed by the British film-maker Joe Wright – his first play after a run of acclaimed movies including Pride & Prejudice, Atonement and the recent Anna Karenina.

The play opens in February, and is followed in March by Mays' next movie. Welcome to the Punch is a cops-and- robbers thriller also starring James McAvoy and Mark Strong. It's the second film by acclaimed young director Eran Creevy, who made his name with the brilliant low-budget Shifty, a tale of friendship and drug-dealing in the London exurbs. Then, in spring, comes another film for Mays, Byzantium, a vampire drama from Neil Jordan, in which the actor stars alongside Gemma Arterton, Saoirse Ronan and Tom Hollander.

Interestingly, all three projects are something like repeat business for Mays. He appeared in both Atonement and Shifty, and was in Made in Dagenham, which was produced by the team behind Byzantium. Forging good relationships with good people, building a platform for future good projects, matters to the actor. "That's always been a pattern in my work."

All told, it adds up to an impressive slate. After a decade of toil in the foothills of TV sitcoms and dramas, of theatre work and low-budget films, he might be on the verge of something like the big time. His recent co-stars aren't surprised. "Danny and I worked on [Jimmy McGovern's] The Street together," Anna Friel tells me. "He was phenomenal in that, and on Red Riding and Shifty. He's from that brilliant Mike Leigh training school, and you can tell. We just work really well together."

Sheridan Smith also testifies to Mays' nuts and bolts experience. Before she played Mrs Biggs, she didn't have a huge amount of heavy drama experience under her belt, "but Danny had done loads. And he's just flawless, so working alongside him, he was a real rock. I was a huge fan from afar, so I was thrilled to be playing his missus."

In 2012, Mrs Biggs, Public Enemies and a year-capping play at the Royal Court – his seventh at the theatre – have given Daniel Mays great momentum. This year, it's about running with that. "With Public Enemies then Mrs Biggs, both those are without doubt the biggest parts I've had to date," he reflects. "You're given an opportunity to take an audience on a journey with a beginning, a middle and an end. I've played a lot of support parts, which is great, and a lot of character parts. And you build up your repertoire with that. But everyone is working up to the point where you take on a lead part. So yeah, it's about now kicking on and trying to do work of the calibre of those dramas, and work that's credible."

Daniel Mays grew up in Buckhurst Hill, Essex. After two years at secondary school, he asked whether he could attend stage school. For his family – he has three brothers; his mum works as the company secretary for his dad's business – his enthusiasm came out of nowhere.

"I think my dad was a bit shocked!" he laughs. "He's an electrician so it was completely left-field. We were all sport-mad – football, golf, all that sort of stuff. I wouldn't say he was reluctant but he was a bit wary of it, I think. But in the end they were very supportive, and I couldn't have asked for parents who did more – they've sacrificed for me, paying fees for me to go to drama school."

Mays spent three years at the Italia Conti Academy of Theatre Arts in London. After taking his GCSEs there, he took a "three-year student course, then three years at Rada – that's a lot of school!".

How did his brothers react to his desire to become an actor? With lots of mickey-taking? "No, never!" he smiles. One is a cricket groundsman, one is in "the money markets in the City, and one is in computers… It's all different walks of life really. But they all come to see the plays. The thing is, I'm incredibly close to them, and I socialise with them a lot. As much as I've got a group of actors I know, I don't tend to hang out with them that much. When the work's so intense, you just wanna switch off from it all."

Once at Italia Conti, he realised his hunger wasn't for performance per se. "Stage school and Rada are poles-apart methods of schooling. Stage school is from the exterior; it's from the outside in. It's tits and teeth, musical theatre, whatever. It was only there [at Rada] that I started doing improvisational classes with this amazing teacher, Denis Noonan, who I'm still very close to. And something just shifted in me. Connected. I knew then that I just wanted to do straight acting."

He remembers sitting in his mum and dad's kitchen, doing an A-level art project. "I still do lots of painting now. But there was a retrospective of De Niro's films on TV. And it was every Sunday – you'd get Raging Bull and Taxi Driver and Goodfellas. And I just stopped painting and I was looking at that thinking, 'Fucking hell, man!' I couldn't quite get my head round the fact that this was the same person playing all those parts. And how much he threw himself into it as well. It was incredible. Because at the end, it is about how much you want to sacrifice," he offers, "or how much you want to put into it. And about not being lazy. Not sticking to what you play time and time again."

Mays knew that if wanted to craft the ability to tackle that kind of range, and do so with any kind of longevity, he needed the "proper" training Rada would give him. The people, the techniques, the launch pad – it was all there. He secured a place, and lapped up his time studying. Ben Whishaw was just below him; Sally Hawkins and Maxine Peake ahead. "But you can count on one hand the people consistently working still from my year. Which," he grins ruefully, "always scares the shit out of me."

In a fundamentally solitary business, Daniel Mays has done his best to build himself a company, or a network of friends and associates. Rather that than fame for its own sake. While he is aware of the need to play the "celebrity game", he can only do so to a "certain extent. I went on Twitter for two weeks then I came off. Cos it was just random strangers going, 'Retweet me, retweet me!'."

He shakes his head. He's of the school of thought that the more people know about his private life, the less they'll care about his characters. "It's counter-productive," he frowns. He looks at his friend McAvoy – his co-star in both Atonement and Welcome to the Punch – as an actor who does things the right way, nicely judging how much PR is required. "James is exceptional in interviews. People like him are confident in selling their product. So you've got to have that in your armour as well. It's a business."

Here in the Royal Court, Mays is secure in the artistic side of things. This well-regarded, long-established hotbed of dramatic innovation makes him feel both comfortable and challenged. "They're like a family to me here," he says, glancing round the bar area. It's filling up for this evening's performances, while over in a corner young playwright Polly Stenham – limbering up for this month's opening of her third play, No Quarter – is huddled with sketchpads and production designers. "I know it sounds wanky, but it feels like coming home. I've got great relationships with everybody in the building. It's just a safe place for me to come, do my thing and grow as an actor."

Hot on the heels of the birth of his daughter, he laughs, the theatre became his bolthole. "Yeah, what I needed to do was come to the Royal Court and have a breakdown every night, just to get me out the house!"

In any case, the daily rigours of theatre work are the best work-out he could hope for. "It's a muscle you've got to come back to, and it's a discipline. It's like playing sport, innit?" says this keen golfer who's still grappling with a handicap of 18. "You've got to turn up and deliver every single night, and sustain that character for two hours. It can only make you a better actor."

At the time of our meeting he was yet to get his teeth into the Joe Wright production. With performances as intense as his, Mays has to consider one job, one play, at a time. But he knows Trelawny of the Wells will be a cracking job, not least because the adaptation has been written by actor-turned-screenwriter-and-playwright Patrick Marber (Closer, Notes on a Scandal).

"I didn't know the play," he admits, "but it's a celebration of the theatre and acting. It's about a not-so-good acting company in Sadler's Wells, and I've got to play a melodramatic, over-the-top actor called Ferdinand Gadd. I'm like, 'Why the fuck is Joe phoning me for that part?'" he jokes. "'Joe, you're off your head!'

"Nah," he smiles, "it'll be great. It's Joe innit, so he's gonna do something radical with it. I think he's gonna use lots of music, lots of songs."

His experience on 2007's Atonement, in which he played a squaddie straggler who falls in with McAvoy in occupied France, feels a long time ago. "But it was incredible. And of course Joe is one of those people you wanna have on your side. It's been great that he's asked me to come back so we can create something together again."

What does he think he learnt making Atonement? "Joe would throw a curveball at you. He's a director who demands everything from you. You've got to be on your toes. One day I remember the phone in the hotel going at seven in the morning. And it was Joe: 'Listen Danny, can you meet me in reception in 10 minutes, I've got something to show you.' He gave me this monologue that Anthony Minghella had written. And we used it in the film – remember when my character is just spouting all that shit? He was somebody who, the way he dealt with his fear and the experience of war, was to just talk, talk, talk, talk. And Joe said, 'Right, can you learn that within an hour? Cos this is the first scene up.' I was like, 'You're kidding me?' So I had to run back to my room and get stuck in."

And now, right now, Mays has to get stuck in again. He checks his watch. He's due back on stage for this evening's performance of Hero in precisely 42 minutes. There's just time to throw some dinner down before he has to dive once more into Jamie's tightly wound, insecure world. If he can switch into the parts so quickly, can he switch them off too? Or does he take them home with him?

"I would say that I hopefully don't," he says carefully. "But Lou would definitely tell you otherwise…" he adds with a guilty smile. But when he does come down with a bad dose of thespianism, well-grounded, well-rounded Daniel Mays can always look to his kids to level him off.

"Mylo don't care if I've done a shit performance!" he laughs. "He's always taking the piss – 'Oh, there's daddy doing the acting!'"

At least Joe Wright is a fan. "The thing I love about Danny is he's incredibly specific, and he has this ability to play these men one wouldn't always associate with having big hearts," the director says. "So I was really excited when the opportunity came up to do this comedy at the Donmar and to play more with that side of Danny's talent. It's a full-on, camp comedy role, and definitely an opportunity for him to be very playful. And he's done a lot more theatre than me – I'll be relying on him heavily. He can teach me how to do it."

'Trelawny of the Wells' is at the Donmar Warehouse, London WC2, from 15 February to 13 April. 'Welcome to the Punch' (12A) is due for release in March; 'Byzantium' is scheduled for release on 3 May