This film has nothing specifically to do with David Hockney, aside from the presence of swimming pools glinting in full-beam sunlight and regular eruptions of water spray as divers plunge in. In fact, this is a remake/update of La Piscine, Jacques Deray’s hothouse psychosexual drama from 1969, featuring Alain Delon and his former girlfriend Romy Schneider, as well as Jane Birkin and Maurice Ronet. It is directed by Italian film-maker Luca Guadagnino, best known perhaps for I Am Love, continuing his unlikely collaboration with Tilda Swinton (who takes the Schneider role, opposite Belgian hunk-of-the-month Matthias Schoenaerts), and together they have concocted a film that is both deeply strange and undeniably funny.

The latter comes mostly by way of Ralph Fiennes, who plays a motormouth producer-promoter type called Harry who shows up unexpectedly in Swinton/Schoenaerts’ sun-washed Sicilian-island idyll. Harry is the former partner of Swinton’s David Bowie-ish silver-jumpsuited rock star, named Marianne Lane: Harry, an apparently amiable figure who’s always chuntering on about which is the best Rolling Stones album or how to find the tastiest ricotta, clearly has a hidden agenda to drive a wedge between Marianne and Schoenaerts’ sensitive film-maker Paul. To this end he has brought along, unannounced, slinky 22-year-old Penelope (Dakota Johnson), who he says is his daughter.

And so the scene is set, against the backdrop of the spectacular rocky landscapes of Pantelleria, for an intense game of emotional chess. Harry, in his blundering way, is always looking for opportunities to prise Marianne away from the group, leaving the brooding Paul and the cut-offs-wearing Penelope alone together. Swinton is on imperious form here, her natural hauteur only amplified by the alpha-female status of her character. There’s an exquisite embellishment to Marianne: having recently had an operation on her vocal cords, Björk-style, she is banned from speaking, and can only produce a hoarse whisper. Not only does this become an early bone of contention in the power struggle between Harry and Paul, it also gives Swinton an extended opportunity to indulge in the graceful, expressive gesturing of the silent-movie actor, or, perhaps more appropriately, contemporary dance.

Swinton also generates weapons-grade chemistry with Schoenaerts – which has the slightly unfortunate effect of thoroughly eclipsing the impact of any relationship pack-shuffling that may ensue. But as strong as their performances are, they are practically burned to a crisp by Fiennes who, since The Grand Budapest Hotel, appears to have located within himself an unrepressable source of manic comedy. Fiennes cuts an extraordinary figure, bearded and largely shirtless (and occasionally trouserless too), almost unrecognisable from the furrowed-brow introvert we have got used to over the years. One extended scene, where he frugs energetically to the Stones’ Emotional Rescue, is genuinely jaw-dropping.

As with I Am Love, Guadagnino has put together something utterly distinctive here, a cocktail of intense emotions, transcendent surroundings and unexpected detours. A real pleasure.