Million Dollar Quartet is a jukebox musical of rock and roll hits pegged to the jam session that really happened at the Sun Records studio in Memphis, Tennessee, one December afternoon in 1956.

The first thing to say is that, after Mamma Mia! and Jersey Boys, jukebox shows that were thoroughly embedded in a theatrical structure with a well-worked narrative, this sort of thing really won’t do. On the other hand, the second thing is: if you’d seen Eric Schaeffer’s production in an Essex pub as a rock and roll tribute night, you’d have had a pretty good time.

So if Cameron Mackintosh wants to turn the Noël Coward into Thursday night in the Pig and Whistle, Benfleet, that’s entirely his business, and good luck to the audiences who help him do that. Even as a lookalike talent competition, though, this is pretty dire.

The quartet are Carl Perkins, Johnny Cash, Jerry Lee Lewis and Elvis Presley – feebly impersonated, respectively, by Robert Britton Lyons (who has come with the show from New York), Derek Hagen, Benn Goddard and Michael Malarkey (last, and indeed first, seen in the Northampton Royal’s Williams and O’Neill plays at the National).

A famous photograph of their session is flashed up as they adopt the same pose. They all sing fairly well, and play guitars – backed by a good bassist and drummer – while Goddard as Jerry Lee pounds a mean piano and raises a few giggles on his under-age womanising but not a titter of recognition when he reveals he’s the cousin of Jimmy Swaggart, the morally hypocritical television evangelist.

Each of them has a reason to be in record producer Sam Phillips’ studio (Bill Ward as Phillips has an Alabama accent as convincing as Jimmy Swaggart’s cringing piety): he’s given them all breaks and now they’re all deserting him for bigger labels. This could have been a dramatic structure, but it’s hopelessly botched.

We run the gamut of “Blue Suede Shoes,” Chuck Berry’s “Brown Eyed Handsome Man,” “Sixteen Tons,” “I Hear You Knocking” (well done by slinky Francesca Jackson as Elvis’ girlfriend), “Great Balls of Fire” and so on; but there’s no point of pressure when each song comes, and it’s not the sort of stuff you want to sit in a seat and listen to. You find yourself hand-jiving, tapping your feet and wanting to scream and shout.

Especially the latter, and after 75 torpid minutes, despite all the frenetic activity, they all give up, too, and the set swings round into a huge lighting bank and a concert encore with a life, and a banality, all of its own. For once it’s worth buying the programme, which tells you much more about the million dollar quartet, and their songs, than the show does.