Jane Austen, meet Frank Ocean. Frank Ocean, Jane Austen. Strange bedfellows? You bet your million-dollar bike. But that's exactly what makes this Persuasion so persuasive: its sheer incongruity. By forcing a faithful script – all prim formalities and literary bon mots – through an ultra-contemporary staging, director Jeff James and his co-writer James Yeatman set up the most jarring of anachronisms and so reveal both past and present anew. Talk about popping the bonnet.

This is costume drama of a different ilk – not regency dresses and silk cravats, but hip high street fashions: pastel polo necks and matte anoraks. And yet, everyone on Alex Lowde's white catwalk stage is Straight Outta Austen. When an aging rocker aristo, Sir Walter Elliot (Antony Bunsee), seeks to make savings on his debt-ridden estate, his eldest daughter objects: "The north wing is my favourite wing." The family up sticks to trendy Bath instead.

At 17, Anne Elliot (Lara Rossi) has all but given up on love. Eight years ago, her then boyfriend Captain Wentworth (strong and stable Samuel Edward-Cook) left her for a life at sea and she's never recovered. Not that her family understand. They'd have her marry – if not for love, then for standing and security. Every time they try to persuade her, Anne spins them round with a squeal and shoves them offstage.

Persuasion picks up as Wentworth returns, ready to wife, but seeking a younger model. He hooks up with Anne's cousin Louisa (Cassie Layton), one of two twins, and whisks the whole family off to Lyme Regis – the Ibiza of its day, as James makes quite clear. I promise you this: There ain't no party like a Jane Austen Foam Party. "Captain Wentworth is in high spirits," one cad observes, as he slips under the bubbles with bae.

The effect of this disconnect is a kind of double-vision. It splits everything in two. Not only does Austen suddenly seem our contemporary, we start to seem like hers. Her characters are like people again – not just literary tropes and lace fans. Austen was writing about human hearts and real emotions, and James restores that by taking them seriously. Rossi makes sure there's no brushing off Anne's heartbreak as old-fashioned feminine folly. She glares daggers at anyone who puts her down or gees her up.

At the same time, James shows how little courtship rituals have changed in 200 years. The steps may be different – dabs instead of do-si-dos – but we still do our dating on the dancefloor, and we still dress to impress. Moreover, and most damningly, there's still a rush to marry as if love has a finish line. Arguably the most absurd thing about Austen's characters is that they don't seem that absurd at all.

Certainly, all this reawakens the satire – reclaiming Austen as a keen-sighted observer, not just a doe-eyed romantic. Sometimes, her final novel even seems to be taking the piss out of her earlier work. Why, Anne asks, are women only of interest while they're picking out a partner? And how often is that still the case? Indeed, as Anne's suitors start circle, Persuasion starts to look a lot like Bridget Jones' Diary.

All this gives a great cast plenty to play with. Helen Cripps scowls as a stressed-out single mum, while her hubby (Dorian Simpson) darts off on playdates. Layton and Caroline Moroney are hilarious as the teenage twins in uncanny blonde wigs, fawning over anything male and trotting through twee-tween dance routines. More than anything else, this is great fun – and that's rarer than it should be.

Persuasion runs at the Manchester Royal Exchange until 24 June.