The real mystery in See How They Run is its mishandling of The Mousetrap

The smell of greasepaint has always pervaded the cinema, from Les Enfants du Paradis and Le Dernier Métro to All About Eve and Theatre of Blood. It was the last of these, with its savage joke of bumping off the drama critics, that occasionally came to mind as I watched the newly released See How They Run: a spoof whodunnit based on the idea that a killer is on the loose, apparently to prevent Agatha Christie’s The Mousetrap being turned into a movie.

The film is escapist fun and Mark Chappell’s script bulges with theatrical in-jokes. The title is identical to that of a 1945 farce by Philip King that contains the famous line, “Sergeant, arrest most of these vicars.” The putative Mousetrap movie is to be directed by Leo Köpernick, which I take to be a deliberate echo of Carl Zuckmayer’s play The Captain of Köpenick. Chappell’s detective is called Inspector Stoppard and at one point, in a reference to Stoppard’s own Christie parody, someone says of a corpse: “He was a real hound, Inspector.”

If I enjoyed the film, it was largely because of the performance of Saoirse Ronan as Inspector Stoppard’s sidekick: Ronan lights up the screen as a naively enthusiastic constable whose head is stuffed with movie-memories and who can’t see a false conclusion without jumping to it.

While Ronan is terrific, I was irked by the film’s lack of theatrical accuracy. One reason why The Mousetrap took off was that it opened in 1952 in one of London’s smallest theatres, the Ambassadors, which seats 453. In the movie, however, scenes from The Mousetrap are shot in the Old Vic, which has a capacity of over 900, and the audience congregate in the foyer of the Dominion which can house nearly 3,000 people. These may seem pedantic points but one loses the sense that much of The Mousetrap’s appeal depended on the cosy intimacy of the Ambassadors where it spent the first 21 years of its life.

I was also puzzled by the film’s pick-and-mix approach to its characters. Three of them are identifiably real people: Richard Attenborough and Sheila Sim, who were in the original Mousetrap cast, and John Woolf, who planned to make a movie once the play closed. Why, though, is The Mousetrap’s producer a fictive female rather than Peter Saunders, who presented numerous Christie plays? Saunders, a tweedy English clubman, was a very engaging character. I remember once writing a piece about The Mousetrap and complaining that, despite the wintry setting, the detective turned up with no sign of snow on his clothes. Saunders told me that was a problem stage management had long been trying to solve. Since the play had already been running for 15 years, I thought it was one they might have cracked.

Related: ‘It’s almost like a soap’: Saoirse Ronan and David Oyelowo on how the whodunnit rose from the dead

In short, I’d have liked the film to have had more period detail. It is set early in 1953, between the death of George VI and the coronation of Elizabeth II. No mention is made of that. The pop songs of the era are never invoked. Above all, there is hardly any reference to radio, which was then the dominant medium. A big factor in The Mousetrap’s early success was that an extract from it featured in a radio programme called Henry Hall’s Guest Night. I know because I heard it and was immediately fascinated by Christie’s play.

See How They Run is a perfectly pleasant movie but it would be even better if it was set in a small-scale theatre and caught the precise flavour of the early 50s.