Tilda Swinton plays middle-aged international rock star Marianne, holed up and domesticated in an Italian villa on the sultry island of Pantelleria with her lover Paul (Matthias Schoenaerts), a sexy and brooding film-maker.

Marianne is recovering from throat surgery and cannot speak, let alone sing; Paul is a recovering addict and will not party. They lie naked in the sun all day when they aren’t making love in the pool.

When Marianne’s ex-lover Harry (played by a ridiculously vivacious Ralph Fiennes, whose versatility in roles never ceases to amaze) shows up with his newly discovered daughter Penelope (Dakota Johnson, who’s possibly taking after her mother Melanie Griffith as being forever typecast as “the sexy character”), things get slippery.

The pacing is slow, giving wide breadth to the stunning landscape cinematography and allowing, too, each eye-squint and smirk to stick to the screen so that the close-ups and the wide-angles, together, create tension.

One could squeeze sexual strain from the celluloid like juice from a lemon here, but there’s not much sting. Even when the tension has an underlying hint of violence, it’s still rather languid.

At times it feels repetitive, as if the denouement will never come. But it does, and when it does, it’s not the end. The film goes well beyond the climax and presents something almost new so that the forbidden love quadrangle lends itself to a cheeky commentary on “those crazy rich and famous types”. And it’s this take on the film that gives it the title, A Bigger Splash, notably borrowed from David Hockney’s painting of a Californian swimming pool, now hanging at the Tate in London.

What we have here is an American-produced film for an English-speaking audience from an Italian director who has adapted it from the French original, and somehow Hollywood didn’t get its chic on and Americanise the whole thing.

This film is all European – in its setting, its score and especially mood. This could take joy-ride audiences by surprise because, given the plot, they might be expecting something racier (though you can’t get much sexier).

A Bigger Splash is the kind of film that audiences of Italian auteurs will savour. It’s a slow-burn. It lingers. It’s more the bubbles that come from the after-splash than the cold spray of water.