Simon Stephens likes his juxtapositions. Just as he called his play about terrorism Pornography, so Nuclear War concerns sex. The first sought out the lust around acts of violence; the other, the violence in lust – even, perhaps, in love. Sex, here, is fusion and separation, fission. Desire is invasive. Orgasms obliterate.

Fittingly, bodies do the talking. Rather than a play per se, Stephens has written a text for (or towards) a performance. Nuclear War is a prose-poem – "a series of suggestions" – intended to inspire action. All the words can be discarded (or not), and replaced with gesture or dance or something else altogether: light, sound, breath, smell. Choreographer and director Imogen Knight twists it into rhythm and shape. Her design team add objects and mood.

Words emerge as a fragmented inner-monologue: "the thoughts scratched onto the inside of my head." An older woman steps out into the city, seeking something. She is seven years bereaved – that being the time it takes for the body's cells to completely regenerate – and though still grieving somehow, she's determined to move on in some way. "I want something different to happen to me today." Something human – perhaps sexual, maybe more. The city seems to promise possibility.

Maureen Beattie sits alone in old pants, watched, menacingly, by four crouched figures in suits. They turn china teacups over in their hands. She pulls on a waxed green jacket and steps into their midst. An anonymous crowd, their faces beneath gas masks and stockings, they press against her, push past her and prowl around her – an abstract impression of the city and its hordes. Men jump out from the crowd, catch her eye, each a possibility – at least momentarily: the bloke in blue shoes on the tube, the guy in headphones drinking coffee. Any of them might, she thinks, spark her back to life, pull her back together. All of them contain traces of him, whosoever was in that hospital bed seven years ago, but they're all thrillingly new – and all terrifying for it. Desire, Stephens notes, is wrapped up in memory. It's always in conversation with death. For better or for worse, sex dissolves the self.

By pushing past language, Nuclear War resists definite interpretation. It's felt before it's fully understood: a swirl of sensations and associations, impressions that race off before you've quite grasped them. Images stick in your mind's eye: figures gorging on tangerines, bricks piling up in somebody's arms. Meaning melts and multiplies. At the Royal Court, where writing rules supreme, that's radical. Less so elsewhere. Tucked away upstairs with a small cast, the experiment feels slightly tentative, even apologetic – more testing ground than all-out attack. Brevity further diminishes its daring and, at 45 minutes, Nuclear War's a slip of a thing.

That's not to suggest it's insubstantial. Together Stephens and Knight capture something of what it is to be a body in a city of seven million bodies. That sense of one's self in the middle of a mass of others; the way individual strangers can seem like a pack. Every city-dweller's felt that – at odds with their surroundings. Like everyone else has all the answers, all their shit together, everything going for them – except you. It's far worse for this woman. The city has transformed in her absence. It won't let her in.

Big crowds can be the loneliest places on earth. You alone feel (and it is a feeling) the thoughts in your head: personal insecurities and private guilts, flashes of lust, laughter and fear. Or grief. They sculpt the city around you, change its timbre, colour it in. When the woman notices flashes of yellow or shades of grey, Lee Curran's lighting warps the whole room – a beige box by Chloe Lamford stuffed with chintz, china and pot plants. The whole world's inside your head, and all the men and women merely robots. Automaton. Objects. Bodies.

Hence: sex. Anonymity's at the heart of Nuclear War: faceless masses in their millions. This woman needs that. In seeking some connection – any connection – she's out to use someone else, either for sex or for something else. Every body becomes a target – a notion entangled with consumption and consumerism - but also, simultaneously, a threat. Beattie licks her lips at the sight of one man, only for him to snap back with a hissed stare. These bodies glint and allure, but they also convulse and flail.

Stephens has explored these ideas before – grief in Sea Wall, urban anomie and atomization in Pornography, sex and the city in Carmen Disruption. Indeed, Nuclear War's protagonist could be Harper Reagan: another grieving woman on a boundary-pushing spirit walk. It's the form that's new and, while Knight's staging gets under the skin, it takes time to do so. At first, it's illustrative – images of the city and its crowds, too deliberately debauched to actually unsettle – but it becomes affective, even immersive, as it simplifies. Elizabeth Bernholz's pulsating electro-score picks up, dance proper kicks in, and suddenly, like the woman herself, we're part of something – inside of it as it's inside of us.

Nuclear War runs at the Royal Court until 6 May.