Forget ‘plebgate' or Chris Huhne's speeding points, the 1963 Profumo Affair was a proper political scandal. It had the lot – shady aristocrats, spivs and spies – and lit a fuse under Harold Macmillan's premiership.

For his latest West End musical, Andrew Lloyd Webber has turned his considerable spotlight on the scapegoat of the scandal, ‘society osteopath' Stephen Ward, who first introduced minister for war John Profumo to showgirl Christine Keeler.

It's a story that goes to the heart of the fast-changing social landscape of the time, and Lloyd Webber - reunited with Sunset Boulevard collaborators Don Black (lyrics) and Christopher Hampton (libretto) - attempts to do for 60s Britain what Chicago did for 20s America.

But, from the reedy opening number "Human Sacrifice" (which begins with the inauspicious lyric "Stephen Ward your friendly osteopath / I can fix your lower back for you"), it all feels somewhat underpowered and, dare I say it, cheap. Richard Eyre's production never truly soars and Rob Howell's designs, framed by drapes onto which archive newsreel is projected, are hardly blockbuster.

The establishing scenes at Murray's club in Soho, where Ward first meets Keeler, evoke 60s kitsch (a jaunty song titled "Super-Duper Hula-Hooper" sets the tone), as Ward - a note perfect Alexander Hanson - drifts around like a kind of James Bond for back problems.

I can't say I share the nostalgic glow Lloyd Webber clearly feels for an era when men ruled the world and girls were just accessories. True, Ward may have been a ‘human sacrifice', but he nevertheless manipulated the teenaged Keeler and Rice-Davies (played rather mutedly by Charlottes Spencer and Blackledge) into facilitating his social climbing. When Ward tracks Keeler down at her home - a shabby converted railway carriage - and snatches her away with the blessing of her mother, it's creepy in the extreme.

The story kicks up a gear when Profumo himself (Daniel Flynn, who neatly doubles as Ward's Judge in the second act) enters the frame at Cliveden, the lavish estate of Lord Astor (Anthony Calf) on which Ward rents a cottage for a pound a year. It's here that the toxic introduction to Keeler, who also happens to be sleeping with Russian spy Yevgeny Ivanov - given a somewhat cartoonish portrayal by Ian Conningham - takes place.

Thenceforth there are some memorable moments; the ensemble's gutsy rendition of "You've Never Had it So Good", replete with gimp masks, whips and dog collars chief among them. But, as the second act descends into a montage of journalistic intrusions, police investigations and the eventual trial, it becomes increasingly difficult to feel much at all for Ward's plight, let alone the raging sense of injustice intended by the authors.

It's a shame, because there's a scattering of strong numbers, including the soaring ballad "I'm Hopeless When it Comes to You" as sung by Profumo's injured wife Valerie Hobson (Joanna Riding - who, interestingly, is signed up to star in The Pajama Game in May). And in an era of Leveson and Yewtree, Stephen Ward provides a timely reminder of the interdependent networks that exist at the top end of society.

But all told, like the Blackpool Chamber of Horrors into which Ward's waxwork is placed after his suicide, there's something oddly tacky and anachronistic about the whole enterprise.