The Drifters Girl review – Beverley Knight leads soaring West End show

On the face of it, this is just another jukebox musical about a band whose sweetly-harmonised hits from the '50s to the '70s include classics such as "Kissin' in the Back Row of the Movies", "Under the Boardwalk" and "Come On Over to My Place". But the sheer exuberance of the production turns it into an extraordinarily enjoyable night out in the theatre.

It centres around the tough-nut Southern girl Faye Treadwell – admirably incarnated by Beverley Knight, in spine-tingling voice and beautifully fitted suits – who marries the band's original manager George, and sets about turning them into a success, and herself into one of the first female African American women in the sexist, racist and all-round resistant music industry.

Her success was based in the fact that, on her watch, The Drifters swiftly became not so much a band as a brand ("like the Yankees"), containing a dizzying succession of singers. The framing device for the show – which follows a fairly straight-forward biographical route – is Faye explaining their story to her daughter (a lively Savanna Musoni), ahead of a court case at which she is fighting for the copyright to the Drifters name.

All of this doesn't matter very much though. Indeed, the weakest part of the show is Ed Curtis's plodding book and dialogue. There's not much dramatic engagement in the story; all the characters who wander through remain outlines rather than people and even Faye is a type rather than fully-explored.

What raises The Drifters Girl is the imagination of Jonathan Church's production, fluently designed by Anthony Ward and lit by Ben Cracknell with fluorescent tubes dividing simple panels into different spaces. Fay Fullerton's costumes are beautifully attentive to detail, taking the characters down the years, from the shiny tight suits of the '50s to the gold flared trousers and wide lapels of their last heyday in the '70s.

Within this setting four utterly terrific singers and actors – Adam J Bernard, Tarinn Callender, Matt Henry, and Tosh Wanogho-Maud – play every part and fill every voice. They are credited as co-creators and in truth, they make the show.

They have enormous fun putting feathers and frilly hats on their hats to impersonate maids and dancing girls, kaftans to appear as Peter, Paul and Mary, and a slouch and a cigar for Ahmet Ertegun of Atlantic Records. But their real power is revealed when they revel in that glorious music, adopting different tones to encompass the styles of singers as various as Ben E King, Johnny Moore and Clyde McPhatter. Each has moments to shine, but Bernard is particularly touching as George Treadwell and Wanogho-Maud mines great emotion from his scenes as the tragic Rudy Lewis, who died mysteriously at the age of 27.

Sometimes, we get the songs in direct performance, with the full routines superbly choreographed by Karen Bruce, and energetically danced with glorious precision, sharply catching each angle of the swooping hand and quicksilver movement of the feet. At other moments, they are used to explain the narrative, as in a showstopping rearrangement of "Stand By Me" which Knight sings as she is left bereft by the death of her husband.

None of it is very deep; it skates along the surface of the story rather than probing or explaining character or time. Even the racism encountered in the South of America and in a Britain where signs proclaimed "No blacks, no Irish, no dogs" is dispensed with lightly in a series of brief scenes. But for stirringly performed music and some dancing that makes the heart soar, The Drifters Girl is hard to beat.