Amy is sometimes cut deep by the sense that she and her family might be life's losers. Things certainly aren't going too well for the mouthy, angry Willesden teenager. A-levels have been flunked, a job in a hairdressers is lost in a volcanic eruption, a childhood friendship has been cut short and her boyfriend sends her out as a housebreaker.

But then Amy meets Glenda, a frail old woman with a fierce sense of justice, and the two form an unlikely relationship. Amy helps with the cleaning in the house that looks like "an Amazon fucking warehouse" and Glenda feeds Amy books and ideas, declaring: "You are not a loser, my girl, until you have truly lost something."

The set-up might be a mite trite, like some kind of contemporary variation on Educating Rita, but this is a play – first glimpsed in a 15-minute version at Theatre Uncut at the Traverse in 2012 – which isn't afraid to wear either its heart or its politics on its sleeve. It's all the better for it in a production by Bethany Pitts played out on a stage stacked with towers of books. It turns out that Glenda has been a little light-fingered herself, rescuing the books from the local library that has been closed because of cuts.

Unexpectedly moving and bubbling with anger, this is a play with backbone which asks urgent questions: why do we write off teenagers like Amy? What do we mean by community? What kind of society is it where we accept that people no longer have free access to knowledge as libraries are closed down? "Of course they want to close them down," says Glenda, "they've nothing for sale." Rosie Wyatt gives a heroic performance, bringing both Amy and the old lady into mesmerising, vivid life, in an hour that reminds that we can change the world beginning with ourselves and our own community.

• To 25 August. Box office: 0131-226 0000. Venue: Underbelly