You Won't Succeed on Broadway If You Don't Have Any Jews (St James Theatre)

There's no business like show business – and there'd be no show business at all, suggests this musical revue, if there were no Jews. A greatest hits compendium of big musical numbers – all of which written by Jewish men, from the 1930s through to the present day – are presented with real panache and affection in a show which also functions as a loose history lesson.

Short, animated clips deliver rather cheesy précis of American history alongside accompanying developments in musical theatre and introductions to key Jewish composers and lyricists. Although lightly informative this is really a flimsy premise, the show being simply an excuse to revel in some of the greatest Broadway numbers ever written.

And it is a joy to watch them fly by with the decades, from "Summertime" to "Over the Rainbow", "Big Spender" to "I Dreamed a Dream"; from Gershwin to Sondheim, Rodgers and Hammerstein to Kander and Ebb… Some choices nod to the high proportion of Jewish immigrant talent in the industry – "Tradition" from Fiddler on the Roof gets a barnstorming performance – but mostly the fact is incidental. And finding more recent example seems to become a strain; from the 1990s, the creators Michaela Stern and Daniel Donskoy turn to TV and films, with songs from Smash and Disney's Beauty and the Beast.

The small stage is rammed, with a seven-piece band across the back wall – lively on the swingier numbers, prettily delicate on the quieter. The cast of 12 are given extra zip by six dancers, hoofing and flapping, shimmying and thrusting across the stage, their high-kicks threatening to send drinks flying in this intimate space. They bring a gloss and sexiness to several big numbers, but the singers are rarely outshone.

Special mentions go to John Barr, whose eye-twinkling "Be Our Guest" prompts grins, and Sarah Earsnhaw's motor-mouthed, comically crazy-eyed "Getting Married Today". Mira Ormala powers into some serious high notes, while Jackie Marks provides an emotion-drenched "I Dreamed a Dream" – the memory of bring the first ever Fantine in the West End possibly helping cut through the cliché.

Although there's no set and few costume changes, this is still a classy outing. But it left me wondering, why not do a full-length musical? Yes, you get all the pick'n'mix good bits, but they build to nothing; there's no story or drive, emotional investment or payoff – just sugary rushes of nostalgia. It means the evening often feels lacking point or purpose. You Won't Succeed… is one for musical nerds, or those seeking good ol' fashioned mindless entertainment – despite the fact that the show repeatedly, in exploring the evolution of the genre, strives to make clear just how innovative musicals can be.

You Won't Succeed on Broadway If You Don't Have Any Jews runs at St James Theatre until 5 September.