Crime & Punishment in Dalston, Arcola Theatre, London

For people who haven't read Dostoevsky's Crime and Punishment (and maybe for some who have), the title of this new, updated stage adaptation may sound a touch inflated and incongruous – along the lines of "War and Peace in Wandsworth" or "Sense and Sensibility in Stoke Newington". But David Farr's riveting reworking swiftly establishes that it need make no apologies for transposing the Russian tale of suffering and redemption to the multiracial north-east London district of Dalston.

Developed from workshops at a local school, the piece is staged at the up-and-coming Arcola Theatre, a converted former clothes factory that is the first venue to serve this community in decades, and that, barely one year old, is already garnering awards. Farr's production, for the new youth-oriented Company of Angels, is located in the ground-floor theatre (there are two auditoria) but the atmospherics are perfect, since you could fully believe that you are down in a cellar in this wide, pillared, low-ceilinged and tenebrous space. The drama's various milieux – dominated by the hero's one-room flat, with its neurotically listing door and filthy freestanding toilet facilities – are picked out of the darkness in sickly pools of light. The ambience is of a nightmarishly pregnable bolthole.

It's here that Farr unfolds a grim but often cannily humour-flecked story that reinvents Raskolnikov, the Russian student and his acte gratuit, as a modern unemployed black youth, unhinged by the hopelessness of his lot, readjusting the novel's elements in order to explore the interracial tensions of Dalston. Powerfully shouldering the very demanding and exposed central role, a vivid and moving Dave Fishley plays Darius, a guy who has gone deranged with resentment. If the law is framed in the interests of the white majority, why, he reasons, should a black man not violate it? But it's not the indigenous whites who are Darius's immediate target. He fizzes with hatred of the Turks who have colonised and improved the locality. He characterises them as the white man's bailiffs and prison guards. To escape from jail, you don't, he decides, have to kill the governor. Hence, Darius's axing to death of a Turkish pawnshop owner who has his mother's silver bracelet in hock, a killing further compromised when he has to slaughter his victim's little granddaughter who blundered in on the bloodshed.

The hero's agonised journey from the partially self-deceived position of believing that the murder was committed for "the higher good of my people", to his remorseful volunteering for punishment, is expedited by three other characters. The little redemptive prostitute, Sonya (for me, the major embarrassment of the novel) becomes Sevgi (Michelle Hallak), a young disaffected Turkish student, jealously monitored by her brothers, whom Darius befriends. This is an improvement, but their relationship feels rushed here and too weighed down with Romeo and Juliet overtones.

Farr has better luck with Raz (an amusing Learie Foster), a cool black dude with a sharp, comic distaste for black whingeing, and with Campbell (a lovely performance from Andrew Melville), a sidelined desk-sergeant, near retirement, who disguises an acute fellow-feeling with Darius and a desire to help him behind gusts of tricksy Scots whimsy. Fully justifying its Dalston relocation, this is a Crime and Punishment with attitude, street-cred and wisdom.

To 2 February (020-7503 1646)