Yet Operation Mincemeat: A New Musical, created by David Cumming, Felix Hagan, Natasha Hodgson and Zoë Roberts of theatrical comedy troupe SpitLip, has gone on to win Olivier and Tony awards in the West End and on Broadway.

This fabulous show, produced in association with Avalon and directed by Georgie Staight, has now arrived at the Alexandra in Birmingham as part of a UK-wide tour and its opening night confirmed that it has earned every one of its plaudits.

It is a song and dance retelling of the true mission to mislead Hitler into believing the Allies were planning to invade Sardinia rather than Sicily in 1943. This involved using a corpse washed up on the Spanish coast carrying false invasion plans that would divert enemy troops and leave Sicily for the taking.

The ruse was devised by a select few at MI5 tasked with allowing the Allies to liberate the island from the German Nazis and Italian fascists – and was based on an idea by James Bond creator Ian Fleming that had lain dormant for years.

The planning takes place in a war room set designed by Ben Stone and lit by Mark Henderson with a map-like background, desks and bank of telephones, with moveable props including desks and a staircase for plotting enemy positions that also ingeniously serves as a club and the exit from a plane.

The props are all manoeuvred by a cast of five actors that play a multitude of roles, taking on different personas and genders, at times at the blink of an eye. You can sense the fun they are having from the sendups of bureaucracy in the style of Yes Minister to the sheer Allo Allo-like farce and the hip hop singing as in Hamilton that propel the narrative and keep the audience smiling.

The frenetic pace and fast dialogue, including lines spoken to the fourth wall, provide a chaos controlled by impeccable timing that makes the sequence of complex historical events even more remarkable and memorable.

Far from making light of sacrifice, the show also provides an emotional kick as the ethics of using a dead tramp as the corpse are questioned and the absurdity of war is rendered up in the writing of a poignant love letter to pin on the body of fictitious Major William Martin in similar persona-switching mode.

Seán Carey and Holly Sumpton complement each other sublimely as a slightly eccentric and diffident Charles Cholmondeley and a maverick Ewen Montagu, who together present their audacious plan to Jamie-Rose Monk’s no-nonsense head of section Johnny Bevan who goes on to gain Churchill’s approval.

Charlotte Hanna-Williams shows a sound knowledge of office politics as the secretary Jean Leslie, while Jordan Pearson standing in from a second cast on opening night plays the matronly Hester Leggatt responsible for the love letter from Martin’s fiancée with aplomb.

Dear Bill and Act as If – the latter in which the intelligence team nervously await the results of their mission – are the most powerful of the twenty songs, while Das Übermensch in which the cast switch sides to dance as Nazis could have come out straight out of The Producers.

Music director Sam Sommerfield leads a four-strong band that sounds like a full orchestra, especially in an hilarious send up of the musical tradition in the Glitzy Finale. This is an unmissable show.