Eleven years ago, 21-year-old University of Wyoming student Matthew Shepard was brutally beaten, tied to a fence and left for dead in a gay hate crime that shook America to the core. But The Laramie Project, Moisés Kaufman’s award-winning play about the murder and its aftermath, focuses solely on the small town where it happened: Laramie, Wyoming.

Devised by Kaufman’s Tectonic Theater Project, it’s a kinetic piece based on interviews with more than 70 Laramie residents and has become one of the most performed plays in the modern American repertoire. UK productions are few and far between but no matter, if they are all as powerful as Wild Oats’ revival at The Space. In this tiny church-cum-arts centre on the Isle of Dogs, director Joseph Walsh has delivered a production that in my view trumps even the HBO film version, which featured the likes of Steve Buscemi and Laura Linney.

Walsh’s eight-strong cast is inexperienced by comparison. But over the course of two hours, each effortlessly takes on a multitude of characters, shifting between old and young, gay and straight, murderer and witness, to build up a picture of a town struggling to stay real while all around are trying to make it a symbol for their own agenda.

The direction is sensitive and uncluttered, allowing Laramie voices to be heard in a way that the media who descended on the town after the murder did not. What sparse choreography there is serves a simple message, as when the cast pile up their chairs to represent the lonely fence where Shepard lay dying.

When they help us light candles representing his final view of Laramie’s twinkling lights, it could be mawkish. But as well as marking Matthew's memory, they are a pledge not to forget. US president Barack Obama finally passed the Matthew Shepard Hate Crimes Prevention Act last month, a full decade after his death. But in the same week here in London, a middle-aged gay man was kicked to death in Trafalgar Square.

The Laramie Project cannot prevent such attacks but it can move, educate and activate those intent on preventing them in the future. This production needs and deserves a central London transfer. I sincerely hope it gets one.