Eddie Marsan says it's only in the last "three or four" years of his acting life that he has received "public recognition." He doesn't mind, despite the fact that it's been some two decades. "I enjoyed it when it came because it felt like vindication for all the times I was rejected," he says. "But ultimately I'm an actor who wants to convince an audience. I don't want to be famous."

His family life in Chiswick seems nicely separated from Hollywood, though he has brought a few mementos back to show his children. The latest is an illustration from Snow White and the Huntsman, a big-budget adaptation starring Kristen Stewart. Marsan plays a dwarf, alongside Bob Hoskins and Ray Winstone – both "childhood heroes" and "the sort of people you can have a laugh with when you're spending five hours a day having prosthetics".

Marsan is, on the whole, a fan of prosthetic make-up. He met his wife, an artist in the trade, on a film set. Two years later in Rome, where he was filming Gangs of New York, he "proposed spur of the moment and made her walk down to the Vatican with me in our pyjamas". Before they left, she painted a picture of the apartment they'd rented.

In front of the painting is a photo of Marsan's childhood friend Ray Antoine. "He was the first person that really got me to leave the East End – psychologically," he says. "I'm very proud that we were boys from the estates, but the danger is we can become caricatures of ourselves and what people predict us to be." Antoine went on to be an art director at an advertising agency in Amsterdam, but died suddenly in his sleep aged 30. "It broke my heart," he says.

Nearby is his script cover book, given to him by Grey's Anatomy's Patrick Dempsey ("When I carry it I feel like a jazz musician"), and the Mark Kermode award he won for Happy-Go-Lucky. "He's the film critic I tend to agree with," he says.

Eddie Marsan stars in Playhouse Presents… Walking the Dogs on Thursday at 9pm, Sky Arts 1. Snow White and The Huntsman is in cinemas on 1 June