We’ve seen a super-abundance — no, a hyper-abundance — of plays based on famous films. But the difference between The Graduate, One Flew over the Cuckoo’s Nest, Billy Elliot, Dirty Dancing and other long-running transmutations is that Patrick Barlow’s version of The 39 Steps is a spoof of the original Hitchcock film — and one that’s proved such a magnet at the box office that it’s now replacing a key member of its cast and has settled in for a long West End run.

What’s the appeal of a show that, on the face of it, is pretty pointless? The programme notes imply that it’s nostalgia for an era when British heroes were courageous, enterprising and morally straight, and starched their upper lips every day. But it’s surely no accident that four actors play well over 50 parts and that one of them, Rupert Degas, is a veteran of Marie Jones’s equally successful Stones in His Pockets, where two men played more than 20 roles. Audiences love to be complicit in theatrical games-playing.

The games become the more elaborate because one of the quartet, Charles Edwards, is confined to playing John Buchan’s archetypal hero, Richard Hannay. He’s decent, tweedy, craggy and all that’s necessary for a chap who goes on the run after being wrongly accused of murder and, having escaped to Scotland and eluded the plods, ensures that the secrets of the nation’s air defences aren’t stolen by (presumably) the Hun. Meanwhile, Rachel Pickup, the newcomer to the cast, brings spirit and charm to two main characters: the exotic foreigner, who is killed after revealing the nefarious plot to Hannay, and the girl to whom he’s handcuffed as he traverses hills, glens, streams and bogs.

Both performers are excellent, but it’s the two other actors who, helped by simple props, turn the show into something truly theatrical. There are dizzying moments in which bulky Degas and spindly Simon Gregor transform themselves within a sentence from harried ticket inspectors to goofy train passengers, or from an excited detective hunting down Hannay to the manager of the London Palladium, where he’s secreted. But they’re also terrific as characters who include a char, a milkman, a ferocious Scots presbyterian, a sprightly landlady and her woebegone husband, as well as (Gregor) the hilariously inarticulate constituency chairman who mistakes Hannay for his parliamentary candidate and (Degas) the cackling baddie betraying Britain to the “master race”.

Yet, oddly, the result isn’t what one would expect, given Barlow’s reputation as that dedicated tease, the founder of the National Theatre of Brent. It’s not remotely as silly as his Charge of the Light Brigade or as lacking in tension as his Wonder of Sex. Somehow Maria Aitken’s production keeps us enjoying the story as well as the tricks, the humour and the send-up of tight-vowelled English derring-do. You laugh — but you also want to know what happens when Mr Memory takes the Palladium stage at the play’s denouement.

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