Reggae Britannia, Barbican, London

"Multiculturalism rules," The Selecter's Pauline Black says pointedly, hours after David Cameron has declared it dead. No one else gives the Prime Minister's comment house-room during this exhilarating, three-hour celebration of reggae in Britain. Look around at the delighted one-time skinheads and rude boys dancing to the heroes that unite them, and the idea seems the product of a fevered brain.

British reggae's lynchpin, Dennis Bovell, is the MC for this celebration of the living past, which faded out in the 1980s when roots reggae and lovers rock lost their grip to digital rhythms. The subtly superb house band show what's been lost with their delicate keyboards and heavy-punching horns, guitar echoes and crashing rim-shots – live rhythms that shift yet stay tight. There's little dub dread, more a relief from pressure in this agile music.

True to history, Jamaican imports dominate at first. The response for Ken Boothe is an instant ecstatic reverence I've rarely experienced, an urgent ovation he fully justifies. He's a suited soul testifier, a vulnerable lover man. His 1974 hit "Everything I Own" feels like a secret exile's song as well as a peerless ballad. "Memories don't live like people do," he mentions as he ends, when it feels like Elvis has left the building. Toaster Big Youth is as remarkable, a white-bearded Rastafari mixing prophetic chat with sexual jerks of his gold-suited hips, a wild card swinging his dreadlocks like Medusa's snakes.

Pauline Black is the first British artist. In a Midlands rude-girl suit of sharp straight lines, she brings 2-Tone's faster, jerky punk beat and the needling New Wave aggro of "On My Radio", to which a platoon of fans jog along. The Specials' singer Neville Staple adds more Coventry sufferation with "Ghost Town", though its writer, 2-Tone founder Jerry Dammers, is a glaring omission. "Proper legend!" someone shouts as the band's infirm trombonist Rico finds the breath to contribute. The ex-singers of Aswad and UB40, Brinsley Forde and Ali Campbell, fare less well, the latter's adenoidal "Many Rivers to Cross" making one long for Jimmy Cliff's sacred version. But lovers rock queen Janet Kay creamily sings the first chart-topper by a black British artist, "Lovin' You", a staging post in the cultural liberation replayed tonight.