The Donmar’s season in the West End comes to end with its high-profile Hamlet. And as befits a Hollywood star, Jude Law is firmly at the focus of Michael Grandage’s production, although whether the play benefits from this is questionable.

Law must be one of the angriest Hamlets ever, when he exclaims “now could I drink hot blood”, you wonder what he could have been feasting on before now. There’s little of the philosopher prince contemplating life’s bigger questions; there’s little of the hesitancy of a man weighing up a host of options. Law’s performance is more suited to Harry Hotspur than to the Prince of Denmark – he’s straining for revenge even before he hears the Ghost’s story. This Hamlet would have killed Claudius, beaten up Rosencrantz and Guildenstern before the interval and spent the second half sending Fortinbras packing.

It’s a contrast to Law’s last performance on the London stage, at the Young Vic in 2002, when he was the rather underwhelming Dr Faustus. Here, he’s a man determined to make the stage his own. He rails at Rosencrantz and Guildenstern, almost throttles Gertrude in the bedroom scene and treats Ophelia particularly brusquely. Law speaks the verse beautifully – if a trifle rapidly at first - and he’s riding high on charisma.

His performance works wonders in lighting up the set: designer Christopher Oram seems to have taken Hamlet’s dictum that “Denmark is a prison”, rather too literally. The play takes place in sombre darkness, the high walls illuminated by a few shafts of light, while the black and greys worn by everyone underlines the gloom.

What’s missing is the political tension, which Grandage underplays. There’s little sign of tension about Fortinbras’ intentions and Laertes is not the focus of a popular revolt. In fact, we’re not quite sure why Kevin R McNally’s rather colourless Claudius seizes the throne – it can’t be for the pomp and there isn’t much trace of sexual longing for Gertrude.

Ron Cook doesn’t really get to grips with Polonius. We see neither glimpses of the wise counsellor that the king and queen nor the garrulous fool that the rest of us do. He seems more like a middle-ranking business manager than a central figure at court. But there’s a fine Gertrude from Penelope Wilton, portraying a woman with real fire in her, who gradually learns the truth about her second husband.

Law’s presence will undoubtedly be a huge attraction for audiences, and he gives a good account of himself. But the best productions of Shakespeare’s great tragedy are those where the play’s political, philosophical and domestic themes are interwoven as one and where Hamlet acts accordingly. That’s not quite the case here.