Romcoms are about love and they want to be loved. Billie Piper’s anti-romcom is about something else – and it wants something else. Rare Beasts is a bold experiment in nerve-jangling confrontation: it has the structure and ingredients of romantic comedy but turns everything on its head. On paper, it could be made by Richard Curtis: there are attractive views of London, an awful date in a restaurant, bittersweet scenes with parents, reflective moments by the river, a Bridget Jones-y media job, a glamorous wedding scene and even a cameo for Lily James. But everything goes wrong. Billie Piper’s movie refuses to read the room; it ignores the traditional cues for comedy and gentleness and the learning of life lessons. It is on a spectrum of its own. The movie screeches when it should soothe; where the heroine should find love, she finds absence; where she should show feminist solidarity, she confesses she still needs a man; where there should be closure, there is nothing. The last time I saw something as bleak as this was at the Samuel Beckett festival in Enniskillen. It isn’t an easy watch but the fierce, focused intelligence of Piper’s film-making is exhilarating. She plays Mandy, who works for a TV production company, sitting around with other blank-faced media professionals pitching terrible ideas. She is a single mum, with a difficult child who may have OCD: this is Larch, played by Toby Woolf. She lives with her own mother, the jaded and cantankerous Marion (Kerry Fox) separated from Mandy’s dad, who is annoyingly still on the scene, unwilling or unable to provide financial support despite preparing for a holiday in Thailand. This is the roguish Vic, played by David Thewlis. Mandy’s troubles start when she goes on a date with an entirely obnoxious man called Pete, uningratiatingly played by Leo Bill. Pete is everything she doesn’t need. He is religious, in a peculiarly pompous and defensive way, he is conceited and self-pitying, he has an unlovely habit of telling Mandy what women want and what they should want. In theory, Pete should be on the screen for a few seconds, one of the awful guys on awful dates that the heroine has to endure before she meets The One. But poor, lonely Mandy has no other takers; her low self-esteem means that Pete’s boorish and misogynistic barbs find their target. And maybe dating Pete would be the mature thing to do. Maybe he’s got a point about women and men. Maybe the situation can be forced into something acceptable by sheer force of will. Maybe it’s absurd to wait for some imaginary ideal man. Maybe Mandy should settle. In a way, Rare Beasts is a 90-minute nightmare-fantasy showing what might happen if you made the wrong choice and got into a relationship with the wrong guy in the montage. In real life that is exactly what people do, while maintaining the fiction of romantic destiny until the end of their days. How has Mandy got into this self-hating situation? She thinks she’s been messed up by her dad, who is casually unrepentant throughout. If Piper is processing something personal in this film, she is doing so with uncompromising inventiveness and force. I also suspect that, like so many people, she is a fan of Paul Thomas Anderson’s much admired satirical romance Punch-Drunk Love, from 2002. But she is doing something very distinctive here, too. Go into Rare Beasts expecting a funny romantic film and you will have a rough time. Go for a challenging, psychological satire and well, you’ll still have a rough time. But you’ll see a smart piece of work from a very smart new film-maker. Rare Beasts is released in cinemas and on digital platforms on 21 May.