Mrs Henderson Presents (Noel Coward Theatre)

Terry Johnson directs the West End transfer celebrating the iconic Windmill Theatre and its girls

Mrs Henderson Presents is an old-fashioned musical in a good way: it celebrates the long-gone Windmill Theatre and its famous Revue-de-ville – front cloth comics, naked tableaux, cheerful war-time patriotism – while telling a story of showbiz survival against the odds.

At the same time, director Terry Johnson's restless book – based on Martin Sherman's script for the 2005 Stephen Frears film starring Judi Dench and Bob Hoskins – keeps you guessing on subjects of censorship, old age, abortion and nudity as an act of political defiance; and the songs of George Fenton and Simon Chamberlain, with artful, witty lyrics by the old maestro Don Black, never settle into cliché or predictability.

The spine of the narrative is twofold: how the rich widow Mrs Laura Henderson (Tracie Bennett, a bird-like figure in specs and grey hair with a Piaf-sized voice and the look and bustle of Lilian Baylis at the Old Vic) and her Jewish, former sock-salesman manager Vivian Van Damm (a slyly brilliant Ian Bartholomew) make a real go of the Windmill; and how the mouse-like Maureen (glorious Emma Williams) falls in love with backstage Eddie (fresh-faced Matthew Malthouse), loses him to the war and becomes the star of the show.

Some threads are left hanging, but most of them come right off, obliterating my anxiety that when the chips were down, the knickers wouldn't be, as in the coy posing of Calendar Girls. We're teased with a sudden switch when Maureen and the girls – baited with the offer of increased wages to bare all – insist the men in the room go first. After a bit of comic dithering, we're suddenly into bare bum territory ("You are Jewish!" declares Mrs H to a cringing Van Damm) and a classical nude tableau based on an art gallery visit.

This is where Mrs H has convinced the Lord Chamberlain (Robert Hands) that if, as in the paintings, the girls don't move – she particularly cites the three big Rs, Renoir, Rubens and Raphael – nudity is beautiful, not provocative. And so it proves, in the sketches of Rule Britannia (evoked in John Osborne's The Entertainer, coming soon to the Garrick), fountains and feathers and the magnificent, glowing, starkers statuesque-ness of Williams advancing downstage against the Nazi hordes, how very dare they!

Jamie Foreman (Derek Branning in EastEnders) just misses the spit and sparkle of the Max Miller-style cheeky chappie comic, but he has a big tie and personality and, on opening night, hailed a 97-year-old Windmill girl in the circle after a line of other brave biddies (only one on a walking stick) joined the curtain calls. It was impossible, at this moment at least, to believe that these women were ever exploited in nude revue.

There's a big shake-up during the Blitz and Mrs H takes to the rooftop to ponder past and future – she's suddenly ill and old – before Maureen re-kindles the Dunkirk spirit with a slightly over-strained ballad, "If Mountains Were Easy to Climb," an oddly jarring echo of a much greater song in The Sound of Music. The sound system at least has sorted itself out by this stage in the evening (too aggressively tinny to start with) and the band in the pit under the musical direction of Barney Ashworth comes through very well, too.

Johnson directs his own show, first seen at the Theatre Royal, Bath, last August, with his customary panache and a few cast changes, well aided by Andrew Wright's neat, period-style choreography and Tim Shortall's atmospheric onstage and back-stage design.

Mrs Henderson Presents runs at the Noel Coward Theatre until 18 June.