Martin McDonagh has a problem. And he knows it. “You can’t go round thinking that you’re better than anyone else,” he grins. “But I do.”

It is not really a problem to twang the heartstrings. But in his case, it is at least understandable. Thirteen years ago, the Irish playwright shot to fame with The Beauty Queen of Leenane, a tar-black farce about a 40-year-old festering in Galway with her acid mother. Critics loved it; so did audiences. Three more plays – The Cripple of Inishmaan, A Skull in Connemara, The Lonesome West – quickly followed. At one point, McDonagh, still just 27, had four shows running simultaneously in London. A few years later The Pillowman, a bloody tragicomedy about a writer under interrogation in a dictatorship, won the Olivier award for best new play.

One medium conquered, McDonagh set his sights on another: cinema. In 2004 he wrote and directed a short, Six Shooter, starring Brendan Gleeson as a bereaved man fending off an oddball on a train. It won an Oscar. His first full-length effort, In Bruges – in which Gleeson teams up with Colin Farrell as odd-couple hitmen killing time in the Belgian town – was chosen by Robert Redford to open this year’s Sundance festival.

But the film – which will be released in the UK next week – has had a lacklustre reception. “McDonagh shows no imagination or fire behind the camera,” was Variety’s verdict. Farrell and Ralph Fiennes (playing the hitmen’s cockney boss) are not on top form; the plot, which hinges finally on a dwarf dressed in school uniform, feels both convoluted and generic.

McDonagh is well aware of the film’s shortcomings. In 2001 he said his ambition was to write between 20 and 40 plays and direct one really good film. “This isn’t it,” he admits. “It’s exactly what I wanted to do with this script. But it took me 10 years to get a play I was completely happy with [The Pillowman, which he first drafted in 1994] and I think I need to do about the same amount of work on film.”

He does not look beaten down by the check to his winning streak. Tall, fit and tanned, with a crop of prematurely silver hair, he looks like a former professional tennis player. He’s charming but quiet, too, almost to the point of shyness. And he does not sound Irish – he was born and brought up in south London. His parents, a builder and a house cleaner, moved back to Galway when he and his brother John (also a screenwriter) were in their late teens, but the boys stayed on.

It was while holidaying in Ireland with his parents that he found the inspiration for his plays by observing the locals. He wrote his first six successful plays in a burst of creativity when he was 24, and had just quit his job in the civil service after five years.

In spite of his success there, McDonagh does not feel at home in London. “I probably felt less of an outsider in New York,” he says. “There the plays were completely welcomed with open arms. Whereas here I’ve always felt it was more begrudging.”

Indeed, he has little time for Britain’s theatrical establishment (or, as he puts it, “men who should be shot”). “It’s just the same old people, the same old faces who’ve been to the same old schools,” he says.

When he started out, McDonagh made it his explicit mission to make theatre more accessible and mainstream. Does he think much has changed?

“Not really, no. And anywhere where it is sexier, it’s in a phony way. I go to the Royal Court sometimes and I think it’s hip for the sake of it. There’s no depth or guts or heart.” He sighs. “The fact is, a bad play is usually a bad middle-class play. There’s still something just middle class about the whole experience. Not that I’m saying all middle-class experiences are bad but . . . ”

It is striking that what seems to inflame McDonagh is not the fate of the very poor, as featured in his plays, but the lot of the impoverished playwright, and in particular the etiquette of patronage. He is proud of never needing to go “cap in hand” to producers, because of his early success. “And I think some people don’t really like that. Especially from someone from a supposedly lower class.”

Although he has been working on screenplays for the past decade, he has mostly been devoting himself to the fate of plays he penned nearly 15 years ago, travelling the world with them, attending as many rehearsals of as many productions as possible.

“If you want your play seen in its best light you’ve got to be there. The times I haven’t done that are the worst productions I’ve had.”

McDonagh is highly concerned with his legacy. A few months ago he met a woman who is now a steady girlfriend, but he is certain he does not want children.

“This shit is it. Some people leave kids behind to take care of the world. For me it’s always been about leaving work behind. In lots of ways I thought my life was saved by the filmmakers I loved [he has cited Terrence Malick, Sam Peckinpah, Martin Scorsese and Quentin Tarantino as influences]. If you’d been inspired by people like that then it’s your job to do the same.”