Braff the medicine man has last laugh

All New People was a hit in New York and is coming to the West End. Its star and creator, Zach Braff, tells Alice Jones he's happy to leave Scrubs behind him

"Cereal and no coffee for breakfast at my house. Never a cappuccino or a latté – that was splurging. Then two slices of pizza and a Snapple for lunch. And a falafel sandwich or maybe a burrito for dinner." Zach Braff, star of Scrubs, indie darling of Hollywood and latterly toast of Broadway, is explaining, in some detail, how he used to live on $10 (£6.30) a day, when he was a fledgling actor. Though it's hard to remember a time when his hapless hospital alter-ego J.D. wasn't wall-to-wall on E4, it was not really too long ago. In 2000, aged 25, with a sprinkling of plays and small films under his belt and $300 in the bank, he was waiting tables at a French-Vietnamese restaurant in Beverley Hills. People would come in for dinner straight from the arthouse cinema opposite. "And they would do a double take and say, 'We just saw your movie. We really liked it'. And I'd say, 'Oh, thank you. Now let me tell you about our specials...'"

Cut to 2012 and it's quite a different scene. Eight and half years on Scrubs has made Braff one of the most recognisable, and bankable, faces on American television. (From 2007 until the show ended in 2010, he was rumoured to be earning at least $350,000 per episode). Today, he splashes out on sparkling water, spaghetti bolognese and a cappuccino for lunch. A trickle of fans hover awkwardly by our table and the waitress asks for a picture when she brings the bill. Dressed in expensive layers of grey wool, he's older and less comical-looking than the rubber-faced J.D., almost a little Eeyorish. I'd been expecting a fast-talking, Noo-Joisey wisecracker but he's more a slow-burn, wry anecdote kind of guy, occasionally making himself laugh – a deliberate ack-ack-ack sound somewhere in the back of his throat. He'd make a fine, if lugubrious, stand-up comedian.

For now, though, his focus is elsewhere. Scrubs has given him the means to pursue his "dream life" and go back to where he started – the theatre. He grew up watching his father, a corporate litigator by day, perform in amateur productions of Hello, Dolly! at their New Jersey community theatre. As a teenager he attended the Stagedoor Manor summer camp where Natalie Portman, Robert Downey Jr and Lea Michele also got their first taste for fame. He was scouted from there, aged 14, to shoot his first television pilot, opposite a young Gwyneth Paltrow – "She was the beautiful high school senior and I was the dorky freshman" – and, aged 18, was cast by his hero Woody Allen in Manhattan Murder Mystery. His first professional adult roles were all on stage – as Fleance in Macbeth at New York's Public Theatre opposite Alec Baldwin and Angela Bassett, and Romeo at the outdoor Shakespeare on the Sound in Connecticut.

When Scrubs ended In 2010, he appeared on stage for the first time in eight years, in Trust, by the American Pie director, Paul Weitz. He played a repressed, disaffected young millionaire who falls in love with a dominatrix at an S&M dungeon and enjoyed the experience so much, he was moved to write his own play. The result is All New People, a four-handed black comedy about Charlie, a gloomy thirtysomething who retreats to a luxury New Jersey beach house in the dead of winter to end it all but whose suicidal intentions are thwarted by a string of visitors – a daft estate agent, a drug-dealing fire chief and an escort.

Braff, 36, describes it neatly as The Breakfast Club for 35-year-olds. It opened off-Broadway last summer, with Justin Bartha (the groom in The Hangover) in the lead and Braff braced for brickbats. "I'm a guy who has been in a couple of movies and is known for a big broad TV comedy. And there I was bringing my first play right to off-Broadway. I'm no dummy – I knew I had a bull's-eye on my back." In the event, he need not have worried: The New York Times called it "sensationally funny".

Now, Braff is bringing it to the West End, leaving behind the Manhattan loft, where he lives with his girlfriend, the model Taylor Bagley, and their two dogs, Scooter and Roscoe. In London, he will take the lead role. He always wrote the part with himself in mind but for New York was advised to step back and concentrate on his script. "I feel like I know the character quite intimately. It's inspired by aspects of my life. I mean, he's suicidal and I'm not and never have been, thank God. But the emotions and the philosophies are all things that have come from me and my relationships."

Certainly Braff sticks to the adage: write what you know. "Sad Jews in New Jersey are my specialty," he snorts, shovelling spaghetti into his mouth. "You probably aren't going to see me writing a screenplay about CIA agents rappelling off a cliff." His debut film as a director, Garden State, was about a disillusioned young actor/waiter returning to his New Jersey hometown. Is All New People a sequel? "This is a different period of my life – being an adult pre-marriage and kids and feeling isolated," he says. "If there is a common theme, it's people rescued by love. I'm a bit of a loner... I know a lot of people but I don't necessarily hang out with many people. I have an intimate group of friends. So that's something I write about – at times feeling lonesome."

Really? To the casual observer, Braff lives a charmed life – successful career, homes in New York and LA, model girlfriend, his own plane ("a little one") – but he assures me the angst in his writing is autobiographical. "It's very silly to think that because you're in the public eye and you have financial success that you don't experience all of the emotions and problems that people without those things have. When you first have a blast of living your life in the public eye, it can be quite terrifying. It made me retreat and become more private – and I have it on a very mild level. I'm not agoraphobic or anything. But I have a nice little nest."

He was brought up in South Orange on a diet of Woody Allen, Neil Simon and professional introspection. His parents divorced when he was at school. One of his earliest memories is of playing with his train set in the basement while his parents treated screaming couples in the living room above. "I couldn't really understand their problems but I was very aware of emotion and angst." He tilts his head up at the ceiling, J.D.-style. Does he think it made him a better writer? "I don't know. But it has made me who I am and made me interested in psychology and in questioning happiness."