Exit West, a novel about migration and mutation, full of wormholes and rips in reality, begins as it mostly doesn’t go on. A man and a woman meet at an evening class on corporate identity and product branding. Saeed is down-to-earth, the son of a university professor, and works at an ad agency. Nadia, who wears a full black robe and is employed by an insurance company, lives alone, rides a motorbike, enjoys vinyl and psychedelic mushrooms. She doesn’t pray. We think we know what will happen next: a boy-girl love story, opposites attracting, secular individuals struggling with the shackles of a theological state.

Now, though, this unnamed city is filling with refugees. Militants are creating unrest. The old world was neither paradise nor hell – one of its parks tolerates “early morning junkies and gay lovers who had departed their houses with more time than they needed for the errands they had said they were heading out to accomplish” – but its terrors are driving out those with ambition and connections. Saeed and Nadia embark on a journey that, like the dream logic of a medieval odyssey, takes them to Mykonos, London, San Francisco.

Hamid, intentionally for the most part, doesn’t exert as tight a narrative grip as he did in previous novels such as The Reluctant Fundamentalist and How to Get Filthy Rich in Rising Asia. Exit West shifts between forms, wriggles free of the straitjackets of social realism and eyewitness reportage, and evokes contemporary refugeedom as a narrative hybrid: at once a fable about deterritorialisation, a newsreel about civil society that echoes two films – Kevin Brownlow’s It Happened Here and Peter Watkins’s The War Game – and a speculative fiction that fashions new maps of hell.

All the same, the novel is often strongest in its documentation of life during wartime, as Hamid catalogues the casual devastation of a truck bomb, the sexual molestation that takes place as hundreds of city dwellers throng to take their life savings from a bank, and the supernatural elation of taking a warm shower after weeks on the road. This is annexed to elements of magical realism and even The Lion, the Witch and the Wardrobe-style children’s storytelling. A normal door, Saeed and Nadia’s colleagues start to discuss, “could become a special door, and it could happen without warning, to any door at all”.

Characters move through time and space like abrupt jump-cuts or skipping compact discs. There are no descriptions of life-or-death journeys in the backs of lorries or on flimsy dinghies. No middle passages. Just the cognitive shock of having been freshly transplanted to tough new terrains. Hamid is deft at evoking the almost contradictory nature of Nadia and Saeed’s digital life (their phones are “antennas that sniffed out an invisible world” and transported them “to places distant and near”), whose broadband freedoms contrast with the roadblocks, barbed wire and camps they face in what passes for reality.

Exit West is animated – confused, some may think – by this constant motion between genre, between psychological and political space, and between a recent past, an intensified present and a near future. It’s a motion that mirrors that of a planet where millions are trying to slip away “from once fertile plains cracking with dryness, from seaside villages gasping beneath tidal surges, from overcrowded cities and murderous battlefields”.

The skies in Hamid’s novel are as likely to be populated by helicopters, drones and bombs as they are by dreams and twinkling stars. Yet his vision is ultimately more hopeful than not. In one of the book’s parallel but alternative universes a suicidal man chooses life. In another, two old men – one Dutch, one Brazilian – exchange a kiss. Most of all there is prayer – prayer for the loss that “unites humanity, unites every human being, the temporary nature of our being-ness, and our shared sorrow, the heartache we each carry”.

• Exit West by Mohsin Hamid is published by Hamish Hamilton (£12.99). To order a copy for £9.99 go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99