A married couple fight over the single prescription they can afford for the Aids medication that both of them actually need. Warring parents wait for their child-soldier son to return home. A woman waits in prison to be stoned to death by her community.

These are tales familiar to anyone who gets as far as the international pages of their newspaper. Yet Stoning Mary is not a piece of reportage from Africa, a record of faraway tragedies written to generate a sad shake of the head and a “What can you do?” Instead, the stage directions are explicit: “This play is set in the country it is performed in” and all the actors are to be white. To make audiences take notice of these disasters, the playwright Debbie Tucker Green, winner of the 2004 Olivier Award for Most Promising Newcomer for Born Bad, has transplanted them from distant lands to the back gardens and next-door neighbours of the here and now. If these “everyday” catastrophes were happening in London, Bristol or Manchester, Tucker Green is suggesting, then nobody would be turning the page, flicking the channel. It would be the story of our lives.

Stoning Mary is not here to give audiences an easy ride. The playwright probably doesn’t have a lot of truck with the term “compassion fatigue”, a phrase that implies that there was some compassion there in the first place, that its owner was so caring and sharing that they wrung every last drop of milky human kindness from it before it was spent. Compassion fatigue is not, however, a term that covers indifference, the tendency to reach for the remote during bleaker news stories, to delete an e-mail petition without even opening it, to stalk past charity collectors in the street before they can catch your eye. It is this kind of behaviour that Tucker Green has in her sights. This is a play that comes from a bright, cold anger at a world that allows such a casual response and, by taking three carefully linked stories, attempts to show exactly how bad lives can become, how badly they need to be acknowledged.

A collaboration with Plymouth’s Drum Theatre, Marianne Elliott’s production boldly lures the audience into a violent and disorientating no man’s land. The characters are all present as the auditorium slowly fills, lurking in a gloomy half-light. The Royal Court’s stage has been extended, seating from the stalls removed, and the surface given a grey, gypsum-like coating, a bleak and ruinous rubble. Each story is given a bright white subtitle — “The Aids Genocide. The Prescription”, “The Child Soldier”, “Stoning Mary” — that is projected above the actors with each sudden scene change. The impact is immediate and intimate, a headline you cannot look away from, human emotion spilling out from behind the flat, stark words.

It might be striking, but if it weren’t for the quality of Tucker Green’s writing it would be the stuff of a clever, campaigning television advert rather than a play; the kind of worthy, righteous concept that could induce a guilt trip to the phone to make a donation, but would lack a longer-lasting impact. However, the language spins Tucker Green’s idea into art. This hour-long play is a verbal stampede, syntactical leaps somehow clearing the gap between what is said and what is meant. At its most explicit, this entails two actors playing one character simultaneously — as the married couple circle round the precious prescription in an intolerable fight for life, they are portrayed as both Husband (Peter Sullivan) and Husband Ego (Martin Marquez), Wife (Emily Joyce) and Wife Ego (Heather Craney), the spoken refracted through the unspoken.

Mary’s older sister (Claire Rushbrook) comes to visit her in prison, her fixation with Mary’s ugly new glasses hiding a world of inarticulate fear: “Since when you gotta thing with your things?” she says, all bullish, neck-led gestures and skittish eye contact. Mary (Claire-Louise Cordwell), meanwhile, on learning that just 12 women signed a petition to save her life, launches into a speech made hypnotic by its jump-lead rhythms, every pause and stutter sparked by new disappointment, new realisation: “What about the burn-their-bra bitches? The black bitches/the rootsical bitches/the white the brown bitches/the right-on bitches/what about them?” The performances, too, are excellent, fearlessly squaring up to Tucker Green’s highly stylised language. Cordwell, all bottle-top glasses and knuckles, more like a bullied schoolgirl than a death-row prisoner, is genuinely affecting as the defiant Mary, promising her sister a “comp” ticket to her own stoning.

Rushbrook crackles with self-pity, anger and fear, repeating her parents’ deadly argument with her own boyfriend, while the parents of the Child Soldier, Ruth Sheen and Alan Williams, convey battered-down, brutalised hope, victims of a domestic and political battlefield. They hate each other, resent each other for the way their son (the shaven-headed, chillingly plausible Cole Edwards) has turned out. The situation might be extreme, but the destructive hostility is all too recognisable as “Dad” attacks his wife for her smothering mother love and, by extension, for her cheap perfume — “The smell of the don’t-cost-much. The smell of the two-for-one. The smell a the been-on-a-bit-too-long.”

This marital agony has nothing to do with geography or poverty or civil war — couples tear each other apart like this all over the world. Yet Tucker Green’s main point is that First World complacency facilitates the growth of Third World troubles. She is not trying to prove that this could happen to anyone — she is too sharp to succumb to the cheap, family-of-man, there-but-for-the-grace-of-God platitude — but that it shouldn’t happen to anyone. It hits hard.

Stoning Mary, Royal Court, SW1, Four stars