This one creeps up on you. If Zoe Cooper's play looks like a country boy meets city girl story, it springs a whole heap of surprises before its done. Surface appearances can be deceptive and, as the play itself points out, stories tend to get streamlined into simplicity. This one is anything but.

Jess and Joe are very different. She's the second-homer in Norfolk for a fortnight a year, with a plummy voice, a tubby tummy and a place at a posh public school. He's the local lad, digging trenches for his dad during school holidays, with a broad Norfolk burr and a meek demeanour. They meet, fleetingly, aged nine; Jess spying on Joe, skinny-dipping in Speedos, the smallest by far of a group of lads. As they grow up, their friendship blossoms, edging towards flirtation year on year.

In a sense, it's a play about privilege. Sunnily played by Nicola Coughlan, Jess is blind to hers, while Joe (Rhys Isaac-Jones) is all too aware of it. And yet, it's her sheltered, cosmopolitan life seems so ordinary, and his rural one, exotic and strange. This part of Norfolk is, after all, the sort of Brexit-voting backwater that seems bizarre to London eyes; a small village where local councillors sermonise against the "contagion" of homosexuality. If it's easy to sniff, Cooper asks why. After all, death is something unexceptional for Joe, just part of life, and he talks of his mother's funeral matter-of-factly. For Jess, it's something extraordinary and immense. Questions of nature and norms bubble away beneath the surface.

In time, they prove integral to a play that flips on its axis. Cooper cleverly ushers us into assumptions, inviting us to think in simple binaries: city girl, country boy; clever, dozy; rich, poor. She lets you think you've got the measure of the play, even – and this is a highwire act – that it's a bit ropey and straightforward. Her writing has a concerted naivety, cannily matched in the clunkiness of Derek Bond's staging. His DIY production presents a child's eye view, as if Jess and Joe have staged their own story. They hammer mic stands like fence posts, and spread dank soil over the office carpet of James Perkins' set.

As the stage gets muddy, so does the play. Its trick is to slowly stir in complexities and, one by one, Cooper picks at, unfurls, and finally overturns those initial binaries. Surface appearances give way to shades of grey. Beneath her apparent privilege, Jess has her issues, just as Joe has his. There's lots going on beneath puppy fat, plum vowels and swimming trunks; all of it normal, all of it natural.

To say any more would spoil the play's power, which rests in wrongfooting its audience. Save to say, this is a play that matures alongside its characters and the more they appreciate the intricacies of life, the bits that don't fit tidy definitions or neat narratives, the more we do too. It's a daring move that pays dividends with a ‘hell yeah' ending; the sort that sets tear ducts going and sends stomachs soaring. You'll want to punch the air.

Jess and Joe Forever runs at the Orange Tree until 8 October, then tours to Watford, Newcastle and Didcot.