When David Tennant plays Doctor Who he relies on one expression. His eyes become bulging marbles, his teeth turn into big white tombstones and his forehead slightly puckers, giving the impression that he hopes to repulse uppity Daleks and other outer-space jetsam with no more than aghast looks, incisors and a wrinkle. But Gregory Doran’s fluent, pacey, modern-dress revival of Hamlet gives Tennant the chance to show the world that he has the range to tackle the most demanding classical role of all – and, praise be, he seizes it.

I’ve seen bolder Hamlets and more moving Hamlets, but few who kept me so riveted throughout. Even when Tennant boggles in wonder at his father’s ghost or dismay at his incestuous mother, his eyes, teeth and steep, furrowed brow don’t do all the acting. Indeed, the first surprise is the intensity of his mourning. He stands there in his black suit and tie, impervious to the champagne drinkers partying beneath their crystal chandeliers, and then, left alone, he twists, half-collapses, crouches, squeals and screeches in an agony of grief, rage and disgust. And then comes the second, concomitant surprise.

We’ve already met Patrick Stewart’s Claudius, a smiling, slippery King who exudes a geniality that, thanks to his sly glances and evident distaste for Hamlet, we know to be spurious. And now we meet his dead brother, who is also Patrick Stewart, but a very different Patrick Stewart. This scarily corporeal ghost circles Tennant’s Hamlet, who has sunk to his knees, and roars out his demands like some monstrous dictator or aggrieved ogre. Even after he’s grimly exited the stage he dominates it, turning his cries of “remember me” and “swear” into ferocious orders, the latter making the theatre quake and shake as much as his former subjects.

Times Archive, 1899: Madame Bernhardt's Hamlet

No-one who is an admirer of Mme. Bernhardt's wonderful art and wonderful personality will come away disappointed

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This leaves you wondering if Hamlet’s father really was a more appealing ruler than his usurping brother. More importantly, it gives added urgency to the oldest Hamlet question of all.

Why does the Prince delay the revenge that he has promised this paternal powerhouse? That’s something to exercise the amateur shrinks in the audience, who will note that Tennant’s Hamlet ends the closet scene by burying his head in the lap of Penny Downie’s baffled, stricken Gertrude, then gives her a needy, imploring look and kisses her on the lips. Yet, praise again be, Tennant isn’t the sort of reductively Oedipal Hamlet who should ideally be stretched out on Dr Freud’s sofa bed. Nor is he one of those Hamlets who, while faking mad, actually becomes mad or half-mad. True, he skims about the black, shiny stage in jeans and bare feet, alarming the court; but that’s a sane man’s calculated diversion. If there’s a nonpsychiatric explanation for his inaction it’s maybe a more traditional addiction to “the pale cast of thought”.

Tennant is restless, curt and mocking when he needs to be, affectionate when he can be, and, apart from an occasional tendency to gabble, pretty impressive. But most noticably he’s so dreamily reflective that you feel that Claudius’s fatal mistake was refusing him permission to resume his philosophy degree in the safety of faraway Wittenberg. Like Gordon Brown, who came to a preview, this very temporary leader is error-prone.

Doran isn’t a director who goes in for gratuitous oddities, but there are one or two in his production. I liked the transformation of the dumb show that precedes the play-within-the-play into a piece of subversive burlesque, with the Queen played by a blubbery, whooping pantomime dame, but I hated the cut that means we get no explanation of Hamlet’s failure to reach England and no mention of his morally questionable destruction of Rosencrantz and Guildenstern.

Almost as bad, Fortinbras makes a final appearance as an SAS general flown in from Norway, but remains weirdly mute, saying nothing about Hamlet or anything else. However, there can be no complaint about the supporting performances, least of all Oliver Ford Davies’s Polonius.

Not that the overall woes of the Polonius family are handled with total success. Mariah Gale, a pleasant, obedient young women who wears pedal pushers, doesn’t seem much in love with Hamlet. Nor does she display the feelings for her father that would explain her madness after Hamlet has, in this updated Elsinore, shot him dead. But Polonius himself is another matter. That old politician is usually either canny and tough or he’s an amiably potty family man. Ford Davies solves the dilemma this presents by being both, now intently eyeballing and lecturing Gale’s Ophelia, now drifting off into a senior moment. With him in top form, Stewart demonstrating his versatility, and Tennant definitively quitting his Tardis, this is a revival to relish.

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