This is theatre of the close-up-and-personal kind. Richard Greenberg's play, first seen in New York in 2002, is a window into the lives, home and minds of two hoarding, eccentric brothers, Langley and Homer Collyer. Played here by Andrew Scott and David Dawson respectively, the bodies of their real-life counterparts were found among a lifetime's junk and jumble in their Harlem house in 1947.

The discovery cemented the siblings into the annals of New York lore, though Greenberg is very quick to confess he did little or no research for his play.

"The Dazzle is based on the lives of The Collyer Brothers, about whom I know almost nothing," he says in his author's note. This is the disclaimer equivalent of having your cake and eating it: that is, tapping into the notoriety of a real-life subject yet absolving yourself of the responsibility to represent it accurately. Clever. And in this case, also rewarding.

Because, without having to worry about details or letting the facts get in the way of a good story, Greenberg is free to explore the tragic self-destruction of these obsessives.

To be a member of the audience in Simon Evans's engrossing production is to be an uninvited guest in the Collyer home. Ben Stone's design suggests the faded grandeur of the brothers' Harlem house with a splash of wood-panelling. But it's the space itself, a pleasingly neglected top floor of a building that was formerly part of St Martin's School of Art, that transports us. It's accessed by climbing a stairwell that revolves around an almost infinitely deep, caged though disused lift-shaft. Even at this height, the Charing Cross Road traffic filters into the building adding to the sense of an outside world hostile to the sensitive souls within. Occasionally, the brothers come under physical attack from neighbours who chuck stuff through the windows, just because the inhabitants are a bit weird.

Both men are super intelligent and entertainingly articulate. Scott's Langley is the talented one. He is a concert pianist whose art qualifies him for the indulgence of others. The others here being his long-suffering brother Homer (Dawson) who protects him from the banality of other humans and a beautiful Fifth Avenue heiress (Joanna Vanderham) who ill-advisedly falls for Langley. Though living with her, Langley concludes, would be no more interesting than living along side a "small uninteresting body of water."

If the play is verbose, it is also brimful of dazzling dialogue. Perhaps most memorable is when Langley describes his and his brother's decline in terms of tragedy. "Tragedy is when a few people sink to the level where most people always are," which is about as brilliant a definition as you could hope for. I wonder what his definition of comedy would be.

Scott, whose screen roles include Moriarty in Sherlock and the conspiratorial C in the latest Bond film, Spectre, is an actor who specialises in the unhinged. And he plays Langley like a high-functioning Asperger's sufferer. Sentences are interrupted by a constant flow of thoughts. And there is that inability to empathise with others, even his brother Homer, whose life has been devoted to serving him.

Indeed, Homer's is the real tragedy here. And Dawson brilliantly captures the bitterness of a man haunted by the realisation that his life has been wasted. By now, the brothers are like vagrants in their own home. And, after their final, moving end, we spill on to Charing Cross Road with a sense of being privileged by the company we have kept and, as is often the case with the most close-up-and personal theatre, slightly shamed by our own voyeurism.