SpitLip’s anarchic adaptation of one of the second world war’s weirdest stories has been working its way up from the fringe for four years now. A West End run is the ultimate proof of concept for this irrepressible musical comedy, and the ingenious ensemble who created and perform it. Its plot is well documented from history books to Hollywood: Britain needed to fool Hitler into moving his troops out of Sicily before their planned European invasion, so the secret service planted false plans on a corpse, and floated it on to a Spanish shore. What makes this version of the real-life spy caper so joyfully smart, not to mention topical, is its focus on the overweening arrogance (and sometimes ineptitude) of the Eton-educated war “heroes” who came up with the plan. Gender-swapped roles underline the satire: Natasha Hodgson’s self-serving Ewen Montagu swaggers around like God’s gift to espionage, ignoring the warnings of his more assiduous colleagues. “Is any of this legal?” asks the ever-anxious Charles Cholmondeley (David Cumming). “Good question,” replies Montagu. “The answer is, of course, never mind.” This is a show that can movingly celebrate the unsung women of the secretarial pool while also allowing them to express their frustrations in a perfectly choreographed Beyoncé pastiche. There’s pathos, too, among the gag-packed songs, including those dignifying the dead man whose body was treated so cavalierly. The tight physical comedy of the fringe original has translated well to the big stage with the aid of incoming director Rob Hastie, and there has been panache and polish applied throughout, from Ben Stones’s new set to a literal “Glitzy Finale”. Only the strength of the performers’ voices is tested by the transfer, but at least they now have the benefit of microphones. Some moments from the fringe show, such as the barnstorming dance number that opens the second half, are simply unimprovable, and the MVP of the five-strong cast remains Jak Malone, who brings effortless distinction to his vastly different roles, from a doughty submarine captain to a camp, creepy coroner. But it’s as Hester Leggett, MI5’s long-serving matron figure, that he steals the show. Whatever is next for this production, expect his rendition of Dear Bill to be breaking hearts for some time to come. At the Fortune theatre, London, until 19 August