Mrs Henderson Presents, Noël Coward Theatre

War bad, theatre good. That’s about the level of insight available from this amiable show, transferring after a successful run in Bath. It’s one of the weaker entries in the ever-popular backstage genre, sharing Vaudevillian DNA with Gypsy and a Nazi backdrop with Cabaret, but lacking the profundity of either. Though our girls bare all to stick it to Hitler, the drama remains skin-deep.

In this love letter to showbusiness, wealthy widow Mrs Henderson (Tracie Bennett) is the evangelical late convert, who decides on a whim to buy the Windmill Theatre rather than invest in a donkey sanctuary: “Actors are just as endearing and twice as needy.” Their non-stop Revudeville, brainchild of Jewish manager Vivian Van Damm (Ian Bartholomew, pictured below), is a hit, but they soon need a new gimmick to get bums on seats. Enter Renudeville, with naked girls posed as works of art in order to evade the Lord Chamberlain’s strict rules. When bombs start dropping, motto “The Windmill never closes” becomes a Blitz spirit credo.

It’s inspired by true events – the Windmill was indeed the only theatre to remain open throughout the 1940s – and it’s heartwarming to see this Soho-set show come home to the West End. (Accompanied, on opening night, by some of the real Windmill girls.) But nostalgic affection can only go so far. Having sanded off the interestingly rough edges of the 2005 Judi Dench-starring film, book writer and director Terry Johnson is left with a slight piece in which wartime rationing seems to have extended to the characterisation.

Our lack of investment becomes problematic in the more serious second half, which also tries to have its cake and eat it by arguing that escapist entertainment is a patriotic public service, but also chiding us for living in a dream world while Europe falls into chaos. The murkiness of that deliberation is best left unexamined, as is the dubious female empowerment that comes with stripping off for England. In fact, the best scene turns the tables on the blokes, as the rehearsing girls demand – ahem – tit for tat from the watching men. Cue a well-placed music stand and jokes about piccolos.

Mrs Henderson is relegated to supporting role in Johnson’s version, and her bracing conflict with Van Damm softened to odd-couple bickering and mutual yearning for a second youth. Bennett provides gravelly charm, but doesn’t get much opportunity to show off her vocal range. Bartholomew is engagingly sincere, while Samuel Holmes brings waspish wit to his broadly camp singer, and Katie Bernstein, Lizzy Connolly and Lauren Hood breathe life into their thinly sketched Windmill girls. Robert Hands’ censorious Lord Chamberlain and his assistant (Oliver Jackson) relish a droll Gilbert and Sullivan number – they rail against “a left-wing Charley’s Aunt with a homosexual slant” – with accompanying Ministry of Silly Walks cavorting. Jamie Foreman is less successful, unable to salvage his deliberately unfunny MC.

As the tea girl-turned-Venus, honey-voiced Emma Williams (pictured left) is the standout turn, finding gravitas in even the most anodyne of Don Black lyrics (her big 11 o’clock number involves the climbing of mountains – though no Mother Abbess in sight). The romance with Matthew Malthouse’s stagehand is rather wan, but choreographer Andrew Wright gifts them a winning courtship routine, the highlight of an efficient period contribution that matches George Fenton and Simon Chamberlain’s pleasant if forgettable pastiche score.

Tim Shortall’s evocative set includes a rooftop refuge and a blasted Tube station during an air raid, while Ben Ormerod’s lighting is key to Johnson’s tasteful reproduction of the nude tableaux. However, the show as a whole is rather too risk-averse, lacking the courage and mischievous subversion it champions. Over at the Garrick, fellow slice of dramatic history Red Velvet argues for theatre as a political act. Cheesy charmer Mrs Henderson Presents is content to keep it a populist one.

• Mrs Henderson Presents at Noël Coward Theatre to 18 June

@mkmswain