“Welcome to the world’s greatest dance show” booms a voice over the glittering Meccano set that is the stage – the sort of claim that immediately evokes thoughts of better candidates for the title.

But that is completely irrelevant. Lord of the Dance has certainly been seen by more people than any other – way over 50 million in 40 countries – and it has to be judged on its own terms. What the show supplies is a feast of high-quality Irish dancing, hung on a slender story. The peaceful life of the ancient clans, united under the Lord of the Dance, is threatened by the evil Don Dorcha and his bully boys. The good guys win, though the final battle, with the two teams tap-dancing furiously, with their arms by their sides as required by this style, hardly looks as though they’re fighting for the future of their world.

Looking around the packed house I didn’t see many people who had forked out an exorbitant £8 for a programme, so those seeing the show for the first time would have been hard put to understand the details of the story. But in truth they hardly matter; it’s the dancing that carries this show, and it’s terrific.

The most varied and enjoyable choreography is given to the line-up of talented girls, who bring a splash of colour into the doom-laden proceedings, and tap throughout with relentless precision. The best of them is undoubtedly ‘The Gypsy’, a soloist of tremendous control, high jumps and an engaging personality which she is able to put over despite the constraints of this dance style.

The Lord himself is an amazing tap-dancer, and a likeable hero. Don Dorcha – a ‘bovver boy’ in ill-fitting trousers – exudes power and menace to such an extent that it’s hard to imagine him losing the battle. There is an enchanting, glittering girl who is ‘The Spirit’. She flits through the story orchestrating the action, and is the only member of the cast allowed to dance freely, using her whole body and expressive arms.

Other notables are the ‘Sorcerers’ – two dancing girl fiddlers, and ‘Erin the Goddess’, a singer who brings moments of tuneful respite amid the amplified tapping.

You will have noticed that I have not identified any performer by name. This is because, despite its price, the programme makes no mention of who they are. Surely people who have bought seats deserve to know whom they are looking at? And, equally, how unfair to ask such a talented cast to perform anonymously.

Lord of the Dance continues until Sunday. (Box office: Tel. 0844 847 1585 and 1588.)