Last week I went to the Arcola Theatre in the East End. Based in a former clothes factory, this large 300-seater in Dalston with a cafe and rehearsal space has crept into the "Did you see?" firmament of London theatre gossip; a venue to contend with, a name to be dropped by other productions, an institution referred to by writers.

Four years after its birth, Arcola, having successfully pushed past the seething mass of London's also-rans with a concerted programme of daring and intelligent productions, is now heading, in an Almeida-esque trajectory, towards a moment on Late Review. Astonishingly, it is still unsubsidised, and must rely on box-office-generated income. However, when your productions get rave reviews in the national press, and special mentions in Time Out, paying your actors and front-of-house staff becomes a possibility, not a pipe dream.

This month, Arcola is showing Carver, five short stories by Raymond Carver, which have been adapted and directed by the towering figure of William Gaskill, boss of the Royal Court in the late 1960s, who not only directed premieres of plays by Hare, Arden and Bond, but also co-founded the National Theatre.

The production reflects this noble lineage; the actors, who double up in roles throughout the night, deliver performances that are taut, subtle and threatening. Carver's intense tales of encounter and division are set in a claustrophobic America, where people drink cream sodas, think a trip to Europe is remarkably daring, and sit in front of giant televisions all night long. The narratives are mesmerising and involving; the company expertly cradles a tiny audience (of which more later) in its collective palm.

In the interval, I meet Arcola's artistic director and founder, Mehmet Ergen. London's bid for the 2012 Games may have triumphed, but Ergen is not wild about the prospect of an Olympic Village down the way. His rent has just been put up by 100 per cent. "The whole area is changing," he comments. "Loft developments are being planned to go up everywhere."

I suggest this might be good for Arcola; after all, the Almeida must benefit hugely from having a well-upholstered bourgeoisie on its doorstep in Islington. It is not a good analogy.

Ergen, who keeps his ticket prices at levels of accessibility (£12 for most shows), that other theatres could only either dream about or, must swing huge sponsorship deals for, tells me he does not want to go the way of the Almeida, or even the Donmar. In his view, the two are dominated by either silky period revivals (Hedda Gabler, Guys and Dolls) or showcases from America's theatrical aristocracy (anything by David Mamet or Sam Shepard). "Or whoever has just won the Pulitzer," he cries.

When Arcola does the classics, as it occasionally does, it insists on relevance: Max Stafford-Clark's forthcoming Macbeth is set in a contemporary African state.

Meanwhile, on with the play. It's meant to be a normal preview night for Carver, but the audience is sparse. One of the actors is standing in for someone else, and performs with the text in her hand. The reason? It's 7 July, and after a day of violence and chaos in the capital, not everyone could make it to the theatre. But the show must, and should, go on, and at Arcola, it does.