He's worked with Steven Spielberg and Mike Leigh, but Daniel Mays has no rigid career plan. It's all down to good characters and good stories

As I'm running late, I can't help thinking that it's just as well Mays is an actor who plays parts that are the polar opposite of his own personality. "Troubled" is probably the polite way to describe the characters he's best known for: the aggressive, abusive Jason in Mike Leigh's All or Nothing; the young heroin addict in the BBC drama Rehab; the tortured Michael Myshkin in the recent TV adaptation Red Riding. The kind of characters who, if you turned up late to meet them, might kick you through the nearest window and think nothing of it.

Happily, the real Daniel Mays is sipping a glass of fresh orange juice (although he will later be persuaded to have a pint), minding his own business, taking it easy. He doesn't seem at all like an actor who's just come back from Los Angeles, where he was directed by Steven Spielberg, or a man who appeared in the Oscar-winning Atonement and much-admired Vera Drake. Mays, it turns out, is affable and charming, funny and smart and endearingly modest. This may be why he's managed, despite appearing in so many high-profile projects and being extremely well thought of in his profession, to stay beneath the media radar. Until now.

His latest film, which opened in UK cinemas this weekend, is Shifty, a gritty drama created by writer/director Eran Creevy which, although made on a budget of just 100,000, looks set to punch well above its weight. Mays is pleased with the film not only because of its strong script and storyline, but because it marks where Mays wants to be – in the starring role.

"I've never had a game plan," he says, with a smile. "I've never thought, 'This is what I should do.' I just want to work with good directors on good characters.

"I've played a lot of supporting parts. The great thing about Shifty, and part of the appeal of doing it, is that it's a co-lead. You want to go on some sort of journey in every part that you do. I've done that in television and in theatre, but it's about wanting to do that more in film. You want something that's got a beginning, a middle and an end so you can take an audience on that journey. I've loved the supporting parts that I've done, but I want to maybe, sort of, try my hand at more lead work."

Mays is completely open about the practical considerations of being an actor. "I turned Shifty down at first," he says. "I always loved the script but, owing to a financial situation… well, an ITV drama came along, an equally amazing piece, and I couldn't turn it down.

"I didn't get any money for Shifty, really, it was a freebie. But thank the gods it got put back and the offer came round again and I said, 'Right, let's do it.'"

Mays is only 31, but he's been acting almost non-stop since he graduated from Rada in 2000. Theatre, TV and film – he's been notching up appearances and plaudits, which is why he can get away with saying things like: "I think they (the team behind Shifty, including Creevy, 32] are a really exciting group of young British film-makers. They've got a really great future ahead of them." That and the fact that he's genuinely nice.

And I'd take his word on it because up until now – barring the Channel 4 comedy Plus One, which received mixed reviews – Mays has hardly put a foot wrong. He might be affable and laid-back in person, full of anecdotes and jokes, but there's nothing haphazard about his approach to his craft. And having worked on projects with both Sienna Miller (the just-completed Hippie Hippie Shake) and Keira Knightley (Atonement), he's seen the price that comes with celebrity and he's not terribly keen.

"I don't relish it all," he says. "When we did Hippie Hippie Shake, the sheer volume of photographers waiting outside (to spot Miller], it was horrendous. Plus the fact that they were there all day.

"You've got to be really careful of that sort of stuff, (because] you're an actor, you've got to be able to switch on a different persona and play a part. There are so many actors (I see on] TV and they're doing it, giving it everything, but all I can see is them and their celebrity, because you see them in the paper all the time, or they're endorsing a mobile phone or a perfume. When you're an actor, you should act."

The kind of actors that Mays namechecks among his favourites are Jim Broadbent and Timothy Spall – "great actors and they've got great longevity" – and there's also a certain director who's played a major part in his approach to acting: Mike Leigh.

Mays has worked with Leigh twice. The first time, in All or Nothing, he'd only been out of drama school for a year, and the second time he played the title character's son in Vera Drake. There are more experienced actors than Mays who have claimed that working with Leigh changed their lives, so what does he think? "It does (change everything]," he says of Leigh's approach. "It educates you in such a different way. It's an amazing experience to go through. Ultimately it's about really knowing a character inside and out, every single detail."

Mays says that working with Leigh is a "rollercoaster", partly because of the six-month rehearsal period and partly because the actors can never be sure whether they're going to appear in the film or not. "Sometimes, you tie yourself in knots and you can't see the wood for the trees," Mays explains. "You totally live on your nerves. You always hear the stories about how you might not end up in the film, those horror stories that have actually happened. I was really dogged that I was going to be in it. I didn't say that to (Leigh], but to myself. I just thought I'd give him everything. We really connected. He's a genius."

Mays was recently in LA, where he was shooting a part in the upcoming Tintin movie, directed by Steven Spielberg. It's a small role – Mays plays one of Red Rackham's (Daniel Craig) sidekicks, alongside Mackenzie Crook – but it was a chance to work with Spielberg and also to work in Hollywood for the first time.

"I'd never been out there before, and I enjoyed it for that," he says, sounding as though there's a whole other story behind the experience that he's not going to tell. "I've got a fantastic agent behind me and she always advised me not to (do it] unless I'd got something to go there for because it can be soul-destroying. "(But] what better job to go out for than to work with someone like Spielberg? It was amazing."

Mays has got an agent in LA now, so is he planning to return to Hollywood?

"I don't know what'll happen. Of course I'd like to go back, I think if you're serious about it you've got to properly give it a go. But I don't want to go out and do something I'm not comfortable with, because I'm really proud of the stuff this country produces and the stuff I've been involved in. Atonement, Vera Drake – they've all been nominated for things and they stand up and are counted. So it'd have to be the right thing."

And with that, you understand how Mays manages to balance working with Steven Spielberg and working on Shifty for no money.

"I've learned to say to myself that it's about not getting ideas above your station," he says. "You've got to give everything to each project. You never know what's going to happen, do you? You can't predict it."

In the fickle world of acting, I'm sure Mays is right, but actually, he never wavered in his desire to be an actor. It might be surprising for someone who's graduated from Rada and been involved in two Mike Leigh projects, but Mays wasn't always the "brooding thesp" type. As a teenager, he attended the Italia Conti stage school in London, whose alumni include Kelly Brook, Russell Brand and Lisa Snowdon, but before that, he reveals, there were Michael Jackson routines and jazz classes at the local dance school in Essex where he grew up, the third of four brothers.

"I used to lock myself in my bedroom and do Michael Jackson dancing – that's where it all started," he says, laughing. "There was always this urge in me to perform. I remember going on a holiday to Center Parcs with my mum and dad and all of their friends. All the dads were having a poker night and all the mums were sitting around chatting and drinking; the kids were playing outside. I went back to the chalet with my mum and got my costume – my hat – and did a whole show for them. I remember going around with my hat and they were all throwing money in it. I've always performed that way."

What about his brothers? He laughs. "One's a cricket groundsman, one's in computers, my little brother's a broker in the City. They all do relatively sane jobs; I'm the only crazy one."

Professionally he may be incredibly busy, but domestically Mays is very settled with his partner, Lou, a make-up artist, and their son, Milo, three. "That's all great," he says, a bit embarrassed. "(Having a baby] really wasn't expected or planned, but we've just embraced it. It was a big shock when it happened, a difficult time. But that happens to a lot of people, and now I wouldn't change it for the world. He's brilliant and he's added so much to my life. Those sorts of things… it's just life, isn't it?

"All those things are going to make you a better actor, anyway. You need that kind of life experience."

Shifty is in cinemas now