Three weeks ago at the Public Theatre in New York, I saw a production of Ford's incest tragedy, 'Tis Pity She's A Whore, which for breathtaking ineptitude could scarcely be improved on. Having made a kebab of his sister's heart, the Giovanni in this version went one step further and daubed the word "Cunt", in giant letters in her blood over their bed of love and death.

While it provided a shocking final image, this gory graffito also made nonsense of the play, cancelling that crucial sense you should get that—however warped and extreme his outlook or actions become—Giovanni still sincerely believes he loves his sister when he murders her.

It's a relief and a delight, therefore, to be able to welcome to London David Leveaux's penetrating and pulse-quickening account of the play, just transferred from Stratford to The Pit. Set in 1930's Italy, it begins with a naked lightbulb picking out a set of rosary beads which lies on the bare stage. Rosary beads feature at the end too. As the last remaining survivor surveys the heap of slaughtered bodies at the aborted banquet, disgusted by the venal Cardinal who has wasted no time in confiscating all the corpses' property for the Church, he drops his rosary beads, with icy contempt, into a glass of wine.

Between those two moments, Leveaux's production vividly underscores how the play, without condoning the incestuous pair, sets the perverse and feted idealism of their love against the flattering background of Italian society's routine cruelties, vowbreaking and hypocrisy.

"Her own brother! Oh horrible!" breathes the manservant, Vasques, a lethal cross in Jonathan Hyde's excellent performance between a Spanish Jeeves and a Mafia member (he kills with the discreet efficiency of a butler uncorking a bottle). But while Vasques is shaking his head piously over the siblings' sin, the piteous shrieks of his female informer, whom he is having blinded offstage, rend the air.

Jonathan Cullen strikingly communicates the weird pathology of Giovanni's love, tracing with deft precision how (once it cuts itself off from all conventional values) the young man's mind starts to become unmoored from reality. It's a production full of sudden surprises and shocks (scenes start with a shiver-inducing abruptness; characters meet precipitiously as though hurled together by a hidden force). One of these swift, unexpected touches nicely illuminates Giovanni's gentle decline.

When Sheila Reid's worldly nurse informs him that his sister is pregnant, he springs back and starts jerking about on the floor with his hands over his face. But then he springs forward to give the nurse a happy kiss. He's de-lighted, not devastated by the news—which indicates the increasing untrustworthiness of his judgement.

Having given a splendid performance as an incestuous sister in Stephen Poliakoff's film, Close my Eyes, Saskia Reeves turns in another one here. In the eerie scene played by the light of one candle, in which the Friar terrorises her with the prospect of hell, she shows you a woman rent apart between conventional fears and continued love of her brother. The general level of the acting is excellent. The New York version turned Bergetto, Annabella's dimwitted suitor and his servant, Poggio, into a resoundingly laugh-free vaudeville duo. Playing the former as a shy, owlish innocent with the emotional age of an none-too-bright child, Richard Bonneville is not only very funny but also surprisngly touching when this character cops the death meant for another.

The bloodbath at the end is not for the squeamish. But it's not just gore galore: the violations get to you on a deeper level than sensation. "That'll teach 'em to behave, huh?" joked the man behind me on the way out. He didn't mean it, though; he just wished, like the rest of us, he could have laughed it off.