Tina: the Musical, the Aldwych, London, review: A stupendous Adrienne Warren seems possessed by the spirit of Tina Turner

Even folk who are inclined to be sniffy about jukebox musicals will be overwhelmed by this one. It has everything going for it.

There are the riches of Tina Turner's back catalogue (the show features 23 songs). There is the inspiring story of an African American woman who was able to overcome severe personal and professional adversity and go on to reach the pinnacle of her profession. And there is Adrienne Warren – the Tony-nominated 30-year-old, here making her West End debut – who gives a portrayal of Turner that is absolutely stupendous.

Warren transmits the unstoppable energy and ferocious charm and she has mastered the trademark mannerisms: the warrior legs-astride pose, the leonine mane-shaking, the stiletto-heeled struts. But it would sell the performance short to describe as just a great impersonation. It's more like a case of possession – by Turner's spirit – so that the songs seem to pour from Warren's own soul. There's no doubting the authenticity of the ache and the grit you can hear in the powerhouse voice.

At the same time, Warren irradiates the show with the joy she experiences in embodying Turner's legacy of hope. Boy, do you root for her. When our heroine stages her triumphant comeback in the teeth of misogyny and racial prejudice, you end up in a whirlwind of elation.

This is not to say that the show – the first musical that Phyllida Lloyd has directed since Mamma Mia! – is without shortcomings. Katori Hall's book feels like a brisk summary of events, as it hops too evenly from one episode to another. We start with the childhood in Nutbush, Tennessee, where little Anna Mae Bullock is cruelly abandoned by her mother. We end with global superstardom – via domestic abuse from her husband and professional partner, Ike Turner, and the wilderness years after she left him when “a fortysomething singing has-been” (as she was described by one person) found herself cold-shouldered by a music industry dominated white executives.

There's never time to dwell on things and give them their full due. Lurching from bumptiousness to fits of violence, the excellent Kobna Holdbrook-Smith is an unnerving presence and he communicates ably the controlling jealousy and toxic possessiveness of this Svengali-figure. Billie Holiday once said that you should never get involved with a black musician because the music industry will have shafted him and he will take out his frustrations. There's nothing quite as pithy or culturally penetrating as that remark here. Instead, there are soundbite-sized periodic indications that he festered with resentment because he was never given credit for being a pioneer of pre-Elvis rock.

The songs are used beautifully, whether to drive the plot forward or drench it in mood – or both. “Private Dancer” is hauntingly repositioned to show how Tina is spurned by executives who get up and exit, one by one, from an exclusionary circle of bentwood chairs. We watch record producer Phil Spector urge her through take after take of “River Deep, Mount High”, and we hear a new Tina emerge as she struggles to obey his orders and stick to the melody. “Better Be Good to Me” becomes a blistering, ironic remonstrance in a time-stands-still sequence before she marries Ike.

The show, which has lovely, blurry designs by Mark Thompson and hard-driving, irrepressible choreography by Anthony van Laast, is bookended by a 1998 concert in Brazil. At the climax, the audience become the stadium crowd she was preparing, at the start, to go and meet. God knows how Warren has the energy left to bring the crowd to its feet with such a rousing set – “Proud Mary”, "Nutbush City Limits”, “Simply the Best”. But she performs as if she'd be able to go on all night. Were she to do so, there would certainly be no complaints.

Booking until 20 October (tinathemusical.com)