SEX, spies and lies. Glamour, guns and gossip. One thing you can say about the team currently in situ at Greenwich Theatre - they sure can pick a good story.

New musical A Model Girl explores the Profumo Affair - the scandal which rocked the nation in 1963 and eventually toppled the government.

The story is well known. War Minister Jack Profumo was having an affair with young showgirl Christine Keeler, who was also sleeping with a Soviet spy.

Rumours flourished, amid security fears in the era's paranoid Cold War climate. Profumo denied the affair in the House of Commons and was then exposed as a liar.

These are the bald facts but the saga contains so much more: Sixties hedonists breaking the shackles of post-war piety, fabulous parties, swimming pool frolics in stately homes, and the dangerous sparks which flew when high society embraced low life. And lurking in the shadows, the sinister presence of MI5.

So why did I not find this production the delicious experience it should have been?

The show's creators have done some thorough research to tell a very exciting story - but every time you're about to turn the page it's time for a song.

There are some great musical moments - especially any involving the divine nightclub madam Maureen, played by Lorraine Bruce, and the highly atmospheric ska/reggae-tinged scenes involving West Indian wide-boy Johnny Edgecombe (Graham Bryan).

But there are too many times where the action is disrupted for yet another unmemorable tune.

The set is a multi-purpose structure of solid-looking, highly polished wooden panels and mouldings - evoking all that was good and bad in the British establishment.

With clever, effective lighting and minimal sets, the space is effectively used to create a dozen locations including a beauty salon, a stately home, a court room, a dingy ska nightclub and the House of Commons.

As well as subtly defining the action, lighting designer Olive Fenwick can do showbiz glamour, with the big chorus girl numbers drenched in sumptuous Follies pinks and purples.

Emma Williams looks perfect as Christine, gives the accomplished performance you'd expect from a West End star, and showcases the wonderful period costumes.

High society pimp Stephen Ward was, for all I know, was fey, sleazy and jaded, so James Clyde's portrayal may be more accurate than John Hurt's in the film Scandal - but it doesn't make such compelling viewing. And his suicide is nowhere near as poignant as Hurt's elegant demise.

Dale Rapley's Profumo has a fine voice and the light, sophisticated humour which reportedly made Jack so attractive - but he lacks the historical figure's legendary charisma.

Star performances come from peripheral characters. Lorraine Bruce's Maureen is chock-full of humour and drama, while Graham Bryan's Johnny makes it clear to see why young Christine fell for the sexy dope-dealing ne'er do well. Both have great voices.

Other parts are handled skilfully by the multi-tasking ensemble.

In moments when my attention strayed, I found myself wondering what the show could be if, say, Cameron Mackintosh got his hands and his millions on it. There's a thought.

A Model Girl is a good show; it's just that it could be better.

A Model Girl, to February 24. Greenwich Theatre, Crooms Hill, Greenwich, tickets £16-£25. Box Office 0208 858 7755 or visit greenwichtheatre.org