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As I’ve battled through its tiny, gridlocked foyer into the cavernous auditorium below, I have often wondered if the Shaftesbury Theatre has a death-wish; but seldom more than last night. Whoever decided to bring the stage version of the film Hairspray to London immediately after its remake has come bouncing on to British screens, gaining rave reviews and, no doubt, audiences for whom one viewing is enough?

Well, if the impresarios have goofed, they’ve goofed happily, for the musical is as delightful as I recall it being on Broadway three years ago and more immediate than it could ever be in the cinema. True, the tale of chubby, chunky Tracy Turnblad, who wears what looks like a lacquered wolverine on her head and thinks she resembles Jackie Kennedy, is unashamedly and, at times, absurdly sentimental. But when Leanne Jones’s Tracy is bounding about the stage exuding all-American resilience and optimism — well, she brought out the inner cheerleader I didn’t know I had.

Her world is Baltimore 1962, a place evoked by dresses vaguely indebted to Doris Day and male clothes seemingly designed for aspiring golfers, and her miniworld is the Corny Collins Television Show, which allows kids to dance and maybe even win the Ultra-Clutch Hairspray Company’s annual Miss Teenage Hairspray Contest.

The musical resembles Grease, then? Yes, but only a bit, for Hairspray is wittier, funnier, more good-natured and, without being pretentious, more morally and politically aware.

Mark O’Donnell and Thomas Meehan’s book is a salute to difference. That’s defined both as being fat, like Jones’s Tracy or Michael Ball as her gloriously bloated mother, and, more seriously, as being black in racially divided Maryland. So our heroine’s aim isn’t only to do well on the dance floor, beating her plastic-doll schoolmate Amber, but to integrate Corny Collins’s show, besting Amber’s ruthlessly ambitious, racially bigoted mother, Velma.

Since Rachael Wooding’s Amber has “acne of the soul”, and Tracie Bennett’s Velma something like spiritual smallpox, it is obvious she will succeed. But anyone would forgive the show’s wishfulness, given the ebullience of Marc Shaiman’s rock, which might have been written for and delivered by Elvis himself, and the quality of Jack O’Brien’s cast, which matches its Broadway counterpart for energy.

There are stand-out black performers in Johnnie Fiori’s magnificent music-shop empress and Adrian Hansel as her son Seaweed and, from Ball’s vast dimpling rhino of a Mrs Turnblad and Mel Smith as his/her not-exactly-wee husband, two actors with enough sly sense of mischief to embellish any upmarket panto at Christmas.

What is surprising is that the show gently spoofs itself and what’s refreshing is the sophistication of its jokes. As friendly and unfriendly whites pack into Fiori’s music shop, someone remarks that “if we get any more in here, it’ll be a suburb”. You wouldn't get lines like that in Grease, Fame or any other ode to American high-school life. No wonder I left the Shaftesbury thinking it was a pretty welcoming place after all.

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