Lift off for the writer with stars in his eyes

I last saw Nick Payne when he was working full-time at the National Theatre bookshop. Fast-forward four years and he has just become the youngest ever winner of the Evening Standard's best play theatre award for Constellations (a Royal Court commission that transferred to the West End in November), is on first name terms with Jake Gyllenhaal (who starred in another of his plays off-Broadway last summer) and is in talks with Hollywood about two film adaptations.

Formidable success has little changed Payne, 28, who was a contemporary of mine at York University. He is a bespectacled, kind-hearted chap whose drive is well hidden beneath a relaxed, softly-spoken amiability. During our interview at an Islington café, he laughs when I remind him of our last meeting. "It was great working at the NT bookshop because [adopts a stage whisper] if there was a play I wanted to read I could just order it, read it, then put it on the shelves. I probably nearly bankrupted the shop in the process."

Clearly amazed at how things have turned out, Payne talks me through the years since university. An MA at Central School of Speech and Drama "because I thought it would at least give me something" was a prelude to living in "an awful flat" with walls covered in mould in London Bridge for £90 a week all-in, paid for by working as an usher at the Old Vic, and then another two years at the NT bookshop. By that point Payne had produced five plays, was on the Royal Court Young Writers Programme and had the first hint of what was to come when If There Is I Haven't Found It Yet was performed at the Bush Theatre in 2009 and won him the George Devine Award. "My agent submitted If There Is... for the award without telling me," Payne confesses. "It was a good thing, actually because I'd never have known if I hadn't won it."

After another of his plays Wanderlust was performed at the Royal Court, the theatre asked Payne to write something specifically for its tiny Upstairs venue. It led to Constellations, a poignant, quirky and impossible-to-sum-up two-hander about a cosmologist and a bee keeper whose relationship spans a myriad of possibilities via quantum multiverse theory; set against the inevitable decline in health of the female lead. Currently being reprised by Rafe Spall and Sally Hawkins at the Duke of York's Theatre, the show garnered rave reviews. The Independent's critic Paul Taylor described his "sense of slightly incredulous elation accompanied by the sinking feeling that, as a critic, one would be hard put to begin to do justice to the dazzling way the play creates its own rules, while at the same time being wise enough not to jettison the old rule book either".

It was the result of a year's hard graft. "I haven't had another commission so maybe they're all like this, but the Royal Court basically said write about whatever you want and then gave me a lump sum," says Payne incredulously. How much? I rudely inquire. "It was nearly £6,000 with half upfront and the rest on completion. It was the only work I had at the time, so there was a real imperative to deliver [laughs], not least to try and get it performed."

The Royal Court's soon-to-depart artistic director Dominic Cooke handled Payne's commission. "He was really good at saying, 'Go wild, don't feel you have to play it safe,'" Payne says, describing his amazement at receiving a phone call from Cooke just 24 hours after submitting the finished play. "He just said, 'It's really great, I think we should do it'. He's very trusting. Initially, understandably, he hadn't quite got what the play was doing," he laughs. "It was because of the way I'd formatted the references to a change in the universe, using fonts. He thought that because I'd used three fonts, normal, bold and italic, that there were only three universes. I had to tell him there are, like, 45."

Payne and Spall, who plays the beekeeper, have been friends ever since the latter appeared in If There Is at the Bush. "I didn't write Constellations with Rafe in mind, but as soon as his name came up I thought, 'Of course'," Payne says. He'd never met Hawkins "but obviously I'd seen her at the movies and really wanted her to do it". For a while it looked as if her schedule would make it impossible. "Eventually we nabbed her. We made her do it," Payne grins.

The playwright doesn't just hobnob with the cream of British theatre these days either. Last year, practically out of the blue, he learned that Brokeback Mountain actor Jake Gyllenhaal was interested in If There Is... "I think what happens in New York is an actor like Jake says to his agent, 'I want to do a play, send me a load of plays' and the agent does. My agent and his are the same – and obviously amazing. They sent him If There Is, which he read and liked, then he came to see Constellations. So then we met for breakfast…" he cracks up laughing. After he's recovered from his giggly bout of disbelief, Payne says: "It was pretty surreal. We met at a hotel in Mayfair that was pretty big and grand. You know you're somewhere posh when you order coffee and there are four bits to it: chocolates, little plates, bread…"

Was he intimidated? "Weirdly, no. But not because the prospect of meeting Jake Gyllenhaal wasn't intimidating. I knew we'd have something to talk about – the play. I just kept thinking 'as long as you don't say anything stupid about plays, you'll be fine'."

Payne spent three months in New York last summer while Gyllenhaal performed in If There Is. He claims to have been pretty hands-off in the production process, only wading in to insist that British signposts Americans might not understand be maintained. "The only thing I changed was a reference to Wetherspoons," he says. He spent the time working on his latest Royal Court commission, this time for the bigger Downstairs theatre, which he's planning to submit this week. So far it is unnamed. "It's had a few titles but I've gone off them all. I'm really crap at titles."

He tells me cryptically about a film project that is in the pipeline ("It's not that I'm trying to be secretive it's just that I'm at that nebulous stage of having a few things I might be doing not really confirmed..."). He says he's adapting a novel he "really loves" for the screen, but can't tell me what it is, saying through laughter again, "Why would I be any good at adapting a novel? There's nothing to say I would be. I just really like the novel."

Payne emails later to say his agent has agreed that he's allowed to tell me that Constellations is in the process of being adapted for the screen. If, like The History Boys, it could make the transition from stage to screen with its cast intact, as Spall and Hawkins surely deserve, it could be fascinating. On stage the changes from one world to the next are carried on the strength of the duo's performances. How it might be rendered in cinematic terms is mindboggling – and could be a pitfall if too much fussiness is injected. But, as he's proven, Payne is a dab hand at moving seamlessly from one world to the next. Stage to screen? No problem.

'Constellations', Duke of York's Theatre, London WC2 (0844 871 7627; constellationstheplay.com) to Saturday