For most British playwrights, having your work staged at the National theatre for the first time would be a pinnacle of achievement. For Howard Barker, it's a kind of defeat. Scenes from an Execution, which focuses on the relationship between a pusillanimous artist and her patrons in Renaissance Venice, is Barker's most famous and accessible play – which, to him, is a problem.

"I'm glad it's being done," Barker says. "But I've got a lot of plays that are better than this." Plays like Victory, a bold swoop through Restoration-era England, featuring a king obsessed with bottoms, and paupers liberal with profanities. Or The Europeans, a gory vision of 17th-century Vienna following the expulsion of invading Muslim forces, in which a raped woman gives birth on stage.

"A good play puts the audience through a certain ordeal," he says. "I'm not interested in entertainment." He does admit to being fond of Galactia, the artist in Scenes, being played at the National by Fiona Shaw: lusty and fierce, she spends the entire play arguing with the Venetian state about the purpose of public art. But the suggestion that she comes across sympathetically fills him with disdain. "I don't like sympathetic characters. Theatre should be a taxing experience: the greatest achievement of a writer is to produce a character who creates anxiety." He'll probably be quite pleased that early reviews, beginning to trickle out on Twitter and blogs, suggest that some audiences are indeed finding the play taxing; there have been reports of walk-outs.

You can see why Barker is so frequently described as chilly. Yet there's something curiously romantic about him. His vision of what theatre should be is outlined in Arguments for a Theatre, first published in 1989 and augmented ever since, as he developed his belief in tragedy as the greatest form of theatre. Although his work is often fiercely political, he doesn't believe, he says, in political theatre. "I don't want to hear somebody's arguments about politics, thank you. Nearly all theatre and all culture now is about projecting meaning. It's very Enlightenment. Go to a newspaper if you want enlightenment: don't go to the theatre."

Although Galactia expresses disgust at the idea of being "understood" by her public, Barker says it's another of his characters, Machinist from Animals in Paradise, who comes closest to expressing his own view – by refusing to express one at all: "I write from ignorance. I don't know what I want to say, and I don't care if you listen or not."

He does, however, care that his work gets performed, which is why he has spent the past 20 years directing his own theatre company, the Wrestling School. Although an ensemble, it effectively operates as a dictatorship. "I'm not interested in collaboration," Barker says firmly. "I'm interested in getting people to realise what I'm telling them." (The Wrestling School lost its Arts Council England funding in 2007; the cut still rankles.)

He comes across as an acutely solitary figure: he has lived alone in Brighton since divorcing in the 1980s, and traces his preference for solitude back to childhood. "A solitary child invents friendships and invents his life. Maybe that habit has become fixed in me. To be solitary is to invent." He spends each morning writing, and most afternoons painting; his most recent work has been inspired by Pontius Pilate and Velázquez's Las Meninas.

If he doesn't care for his audience's enjoyment, why should anyone watch his work? His answer is typically singular. "If you have a soul – does everybody have a soul? I don't know – but if you do, then there's a necessity for it to be exposed to things. Theatre is a safe place to expose it."