I can't say I know much about the Disney version of Aladdin, which was released in 1992 at the exact point when I was too old to care for animated films and my children were too young.

So it was a pleasant surprise to encounter this musical, altered and much expanded from the movie, with a book by Chad Beguelin, music by Alan Menken, and lyrics by Tim Rice, Beguelin and the late Howard Ashman. The plot – poor boy falls for rich princess, meets a genie and overcomes all obstacles to true love – remains cartoonish and paper-thin. But the sheer bravura of the production papers over all the cracks. It has a kind of delirious silliness that makes you go with the flow, try as hard as you might to resist.

The real star of the show, first seen on Broadway in 2014, is Bob Crowley's design. Here are acid colours so bright you need sunglasses, sequins that dazzle, wide vistas that conjure visions of palm trees and palaces, and the bustling marketplace of Agrabah where "even our poor people look fabulous" and "by the way, everybody sings."

That knowing tone imbues the entire evening. "What's wrong with a woman running the kingdom?" shouts Princess Jasmine, stamping her pretty foot and refusing to marry any "Tom, Dick or Hassim". "Talk about living in a fairy tale," sneers the evil Jafar (wonderfully camp Don Gallagher), before going off to practise his evil laugh with his sidekick Iago. "Just don't over do it," he warns.

There's nothing subtle about any of it, and panto is never far away but there is a lot of mischievous warmth and production numbers that throw everything including streamers and fireworks into the sheer effort of making everything look, sound and feel as big, brash and all-embracing as possible.

As the Genie, Trevor Dion Nicholas, the only transfer from the American cast, brings his own brand of Broadway razzle dazzle to leading the charge. From the moment he appears as the Genie in Crowley's astonishing golden cave, he flings everything into making sure everyone has a brilliant time.

Led by him, "Friend Like Me" starts as a song and becomes an extravaganza, morphing through a tribute to jazz greats such as Cab Calloway, flinging in a medley of previous Disney hits, and ending up as a full, show-stopping tap number that would make Busby Berkeley blush. The second act opener "Prince Ali" is nearly as extreme, while "Somebody's Got Your Back" is a mad tribute to the boyish bonhomie of the Road movies, complete with slapstick clowning.

Quieter but just as breathtaking is the Oscar-winning "A Whole New World", where Jasmine and Ali ride a magic carpet in a dark velvet, star-filled sky that seems to fill the theatre. The sense of flying – courtesy of the illusion design of Jim Steinmeyer – is so beautifully complete that it's almost possible to ignore the fact that neither Jade Ewen and Dean John-Wilson have the most lovely of voices. Since she is a former Sugababe this is slightly odd, but it may have something to do with the way they have been asked to adopt cod-American accents, which seems most surprising in a show that acknowledges its British audience with references to Strictly Come Dancing and Tommy Cooper.

But both are attractive actors and it is a small cavil about a show that by the sheer force of its geniality, works its magic.

Aladdin is booking at the Prince Edward Theatre until February 2017.