Human Animals (Royal Court)

Pigeons are dive-bombing pedestrians. They're slamming into windows. Foxes are biting back, spreading disease through the city. The birds have stopped singing, and the humans have barricaded themselves in their homes. London is under attack.

Stef Smith's play, a dark, surrealist parable with shades of JG Ballard, is a sideways look at the us-and-them mentality rising through our world. It imagines an invasion, and follows six Londoners as their city comes under siege. In the face of attack and epidemic – a rising hysteria that spreads through the streets – people fight back. They blockade the bridges, and build walls across roads. Animal corpses are piled up in pyres. Parks are set ablaze; habitats destroyed.

A young couple, Jamie and Lisa, start an animal sanctuary in secret. When a pigeon clatters into their window, Jamie (Ashley Zhangazha) takes it in, nursing the bird back to health, but his open-door policy puts their relationship under strain. A mother and daughter, Nancy and Alex, come down on opposite sides; the younger (Natalie Dew, outstanding), just back from travels overseas, protests against animal hostility; the elder (Stella Gonet) fears for her family and her home. Two men, John and Si, meet for drinks in a pub – strangers with a sexual tension become mutually suspicious friends.

This is the language of vermin: hate-speak that dehumanises. It is Katie Hopkins on cockroaches, David Cameron's migrant swarm, Hitler's parasites. But Smith's smart enough not to dismiss that outright, seeking to understand, not just to condemn. Human Animals is a behavioural study, one that examines our need to protect those closest to us, and it suggests that our fear of the other is driven by love of our own.

That's human nature, and Hamish Pirie's staging reveals people as pack animals, driven by familial bonds, pheromones and a compulsion to survive. Camilla Clarke's lurid design puts them in a giant insect cage, basking in the artificial light just like the live crickets and lavae in miniature model boxes around the stage. As pigeons hit glass, paintball guns blast the Perspex back wall. A backdrop of red and white – the colours of nationalism – creeps up on us unnoticed.

True, metaphor overwhelms plot and Smith's narratives tangle and fray as the play goes on, but what seems initially like a straightforward analogy – outsiders as animals – shot through with mordant humour, blossoms into something richer. This is as much about Europe's migrant crisis as Syria's civil war – any environment that drives people out – and Smith swirls in ideas about homophobia, profiteering and the sustainability of activism. It overloads the play, but leaves lots to mull over. By linking ecological conservation with political conservatism, Smith taps into two potent contemporary fears and, if Pirie's production is tattily over-active, it's also skin-crawling and sharp.

Human Animals runs at the Royal Court Upstairs until 18 June.