A murder occurs right as “See How They Run” begins, and for a very good reason: it’s a whodunit film about a real murder backstage at a whodunit play where all the murders are fake.

Got that? Good. Shall we continue?

Sam Rockwell and Saoirse Ronan star as police officers who must unravel this knotty mystery in early-1950s London in a film that’s as much a valentine to whodunits as an indictment of them, and it’s not always clear which side the filmmakers are on.

There’s a touch of noir, some mocking of the murder mystery tropes, a dash of self-awareness, lots of fedoras and coats, mannered humor — “Poppycock!” says one character, “Hitchcock, actually,” comes the reply — and an archness that keeps everything at arm’s length.

All in all, a pleasant diversion, if not a particularly memorable one, all employing upper-class British accents as thick as Devonshire scones. It seems perfectly designed for folks who adore Acorn TV and PBS British mysteries. You know how many celebrities decide to star in kiddie films so that their children can finally appreciate what they do for a living? Well, “See How They Run” is for their grandparents.

It kicks off backstage in the West End at Agatha Christie’s “The Mousetrap,” a mystery that in this telling has celebrated 100 performances and Hollywood is noticing. But there’s a catch: No film adaptation can be made while the play is still running. That may lead to some sabotage.

When the malignant, would-be film director, a delicious Adrien Brody, playing the only American, ends up the victim of a murder — sorry, that’s a MU-dur — Rockwell and Ronan show up to solve the crime. He is a steely-eyed copper who drinks too much, and she is a nervous novice prone to jumping to conclusions.

The early death of Brody’s character doesn’t mean he’s out of the movie. He’s our narrator, snacking on the dialogue as if it were an overstuffed pastrami sandwich. “It’s a whodunit,” he says at one point. “If you’ve seen one, you’ve seen them all.”

Also along for the ride are Ruth Wilson, Reece Shearsmith and Harris Dickinson. There’s also a fancy intellectual screenwriter played insouciantly by David Oyelowo, who is derisively called “London’s most sensitive writer.” It is a hoot to see him play insufferable — as it is to see Ronan do comedy.

Director Tom George and screenwriter Mark Chappell revel in the time period; the cars and furs, and vintage dialogue speckled with “Darlings” and “Hop to it!” This is a film for you if you like your police officers extremely polite. “Constable,” says Rockwell to his partner. “Inspector,” the underling replies. They do this approximately 400 times.

It is a film that adores commenting on its own conventions as it folds in on itself, as when stage props fool savvy characters or when it introduces a flashback and Oyelowo’s screenwriter complains that such a device is “the last refuge of a moribund imagination.” Somewhere in here is an indictment of Hollywood, but it is as blunt a weapon as the one that does the murder.

The filmmakers employ all kinds of ways to try to keep viewers interested, like split screens, some farce and a surreal dream sequence, but there’s not enough humor or grit or anything other than actors swanning around in period clothing.

“See How They Run” fits perfectly in a vibe right now. “Only Murders in the Building” on TV and “Knives Out” at the movie theater add to the list of Kenneth Branagh’s Poirot adaptations, along with “Murder on the Orient Express” and “Death on the Nile.” Whodunits are hot. If you’ve seen this one, you’ve definitely seen them all.