English National Opera may have been given a stay of execution but it knows it has to keep fighting to justify its existence, and its latest revival of Bizet’s Carmen throws a well-aimed punch. Calixto Bieito’s staging, first seen here in 2012, has become one of his most enduring at theatres worldwide, and with reason: the Catalan director’s penchant for shocks and violence is right at home in an opera with menace lurking behind every good tune. Alfons Flores’s stark, black set design conjures imposing atmosphere economically, with a gallows-like flagpole, a phone box you can almost smell or a huge Osborne bull. When the stage briefly fills up with the smugglers’ messy fleet of 1970s Mercs it seems almost comically crowded.

The soldiers in the opening scene set the tone: full of pent-up testosterone, they are not only dangerous but dangerously childish. The women hold their own, however: this staging may have originated pre-Weinstein but, while there’s plenty of casual cruelty, thanks to Jamie Manton’s skilful revival direction it doesn’t feel overly voyeuristic. Manton gets some cracking performances from his cast – the final scene is fingernail-gnawingly tense even though you know what’s about to happen – and Christopher Cowell’s English translation comes across clearly.

Returning as Don José, Sean Panikkar sounds a little lightweight to begin with but grows in vocal stature as his character disintegrates. He’s riveting at the end. Carrie-Ann Williams makes an impressive ENO debut as a late stand-in Micaëla, her top notes big and radiant, her softest passages slightly too quiet – as are Nmon Ford’s low notes as Escamillo, though he has a lithe swagger otherwise. There’s vivid support across the cast, especially from Keel Watson’s arrogant Zuniga, and an exuberant children’s chorus drawn from nearby St Joseph’s Catholic Primary School.

But everything revolves around Carmen. Ginger Costa-Jackson, another ENO debutant, is magnetic. She sings in a strong, wine-dark mezzo-soprano and knows how to hold the stage through stillness. In her Habanera and her other big solos she never seems rushed; the world goes at her pace, thanks to the subtle breathing space that Kerem Hasan’s conducting affords her, and the precision of the orchestra’s response. They, the enlarged chorus, and indeed the whole company, are on fighting form.

• At the Coliseum, London, until 24 February.

• This article was amended on 3 February to clarify the school from which the children’s chorus were drawn.