Maxine Peake is far from being the first woman to play Hamlet. Of those I've seen, Frances de la Tour had a bravura swagger while the German Angela Winkler exuded the vulnerability of a damaged child. Peake goes for neither of those options but plays to her strengths, which is to say that her Hamlet, in Sarah Frankcom's modern-dress production, is caustic, watchful, spry and filled with a moral disgust at the corruption she sees around her.
In appearance, Peake has cropped hair, a shapeless blue suit and a look of wary suspicion. She doesn't go out of her way to underline Hamlet's maleness: character, you feel, matters more than gender. It is, however, noticeable that Peake reacts with anger when told her mourning is "unmanly grief". And even before she has encountered the Ghost, she makes her feelings about Claudius plain by ostentatiously turning her back on him in court. This is clearly a Hamlet with his own built-in bullshit detector.
But what is fascinating is how Peake's performance develops in power in the course of the evening. She beats the ground in fury on hearing of her father's murder. She treats Ophelia with a regretful disdain on realising she has become a stool pigeon. And she turns on Gertrude with downright hostility and physical nausea in dwelling on "the rank sweat of an enseamed bed". Even if "To be or not to be" comes so late in the evening that one thought someone might have mislaid it, this is a fine performance that confirms Peake's capacity for emotional directness and a fierce, uncensored honesty.
But Peake's Hamlet is only one example of cross-gender casting.
Gillian Bevan plays Polonia who here becomes a self-important court official in a trim business suit, while Claire Benedict is a forthright Player King and Jodie McNee a tattoed, punkish Rosencrantz. But of all the sexual switches one of the best is Michelle Butterly as the First Gravedigger who uses a strong scouse accent to underline the character's piss-taking scepticism.
The effect of all this is to give the play much greater tonal variety than it usually possesses. My main reservation concerns the excision of almost all the play's political context. We get no sense that Denmark starts out preparing for war with Norway and that Hamlet's dilemma is only one problem in a court in the midst of a crisis. By cutting the character of Fortinbras, Frankcom also omits a vital opposite to Hamlet: a man fully committed to purposeful action and endowed with a strong sense of realpolitik.
This is a personal rather than a political Hamlet. But, having said that, the production goes out of its way to avoid cliche: on "Alas, poor Yorick" Hamlet gazes at a rolled-up sweater rather than the familiar prop-skull. And, although cast according to gender-convention, there are good performances from John Shrapnel as Claudius and the Ghost and Katie West as Ophelia. I especially liked Shrapnel's quiet menace as Claudius and his ability, as Hamlet's father, to suggest that he was reliving the torments of his murder. And West's Ophelia, a subdued girl driven to self-mutilation and naked self-revelation, hit the mark.
In the end, it is a mixed production that, even at three-and-a-half hours, omits a good deal. What it gives us, however, is an excellent Hamlet by Peake that proves the character has the miraculous ability to take on the colour, style and personality of whoever is lucky enough to perform it.
• Until 25 October. Box office: 0161-833 9833. Venue: Royal Exchange theatre, Manchester.
• At her Peake: the star's stage career in pictures