Is Jude any good? That is the question, as Jude Law opens as Hamlet in the West End. I’m also wondering whether ’tis nobler in the mind to have a quality ensemble cast, or suffer the slings and arrows brought to the production by red-hot celebrity. This is, after all, Britain’s second screen-idol Hamlet this year, following David Tennant’s acclaimed performance in January. Clearly, the play’s no longer the thing.

That’s enough Shakespeare pastiche, and of course it doesn’t matter whether Jude is any good, because Wyndham’s Theatre is sold out, such is the pulling power of his name. Law, I mean, not Shakespeare. Yet Law’s performance is intense and internal rather than declamatory and he illuminates the meaning of every line, a clarity that may stand well with the younger audience that this production is sure to garner.

Law’s lack of obscurity results in a strange, multilayered experience where you cannot help but see Hamlet and his own ghosts from past films. There’s Alfie, as Law appears in a slightly sleazy raincoat; there’s the bravery of the grey soldier from Cold Mountain in the final sword fight; and up pops the young buck of the Primrose Hill Set, as Law tells Ophelia “Get thee to a nunnery” and you inadvertently hear “Get thee to the Priory”.

This afflicted Tennant, too, but with his previous stage career holding him aloft at the RSC he pulled off one of the best Hamlets yet: intelligent, manic, commanding, even funny, with the callow touch that befits the not-so-great Dane. In the celebrity combat, the battle of the Hamlets, Tennant bore his burden better, with only the occasional moment of pop-eyed Doctor Who surprise.

Pity Tennant and Law, two men in their thirties who do not merely bring baggage to the show, but a roll-along suitcase of past images that trundles across the stage behind them. It was the same for Ralph Fiennes in his powerful Hamlet at the Almeida more than a decade ago (when, incidentally, he fell in love with Francesca Annis, who played Gertrude). These are actors who must work twice as hard to slough off their public clichés.

On the other hand, this extra sheen of fame works brilliantly in Hamlet of all plays. Tennant and Law would be quite wrong right now as Shylock or King Lear, but Hamlet is, after all, himself a celebrity in Denmark, the people’s dashing young prince, the centre of all attention. When Hamlet kills Polonius, the court hushes it up because the popular heir to the throne can’t be seen to be sullied. As Claudius puts it: “He’s loved of the distracted multitude,/ Who like not in their judgement, but their eyes.”

The present-day distracted multitude is thronging round the stage door when I wander round after the performance: micro-skirted girls giggling, phones raised aloft ready for a snap when Law comes out for autographs. It was the same for Tennant. You can see the tributes to the “Hamlet Hunk” on YouTube. “It’s homework!” says one teenage scholar in delight.

It’s possibly the best thing to happen to Shakespeare in years. A little Heat and stardust has pumped new life into British theatre, once staggering between touristy musicals and obscure high art. More than 14 million tickets were sold in London last year, proof of a widening audience.

Naturally, some thespian grandees are extremely snotty about the Doctor Who/Alfie nexus. The director Jonathan Miller, miffed that his Bristol production of Hamlet was not invited to the capital, recently railed against “the West End’s obsession with celebrity” and said of Law’s prince: “I suspect he can’t act better than the young unknown who played him for me, who was quite extraordinary.”

Miller is wrong. Law, once he relaxes from the discomfort of press night, will find a fresh, ravenous audience, whose language he speaks: “Hamlet is a bit like a great song that’s been covered by a load of different singers,” said Law, simply. “It’s like Bob Dylan, Van Morrison and Joni Mitchell all covering the same song. But they would each bring a different sound and colour to it.”

Law seems weighed down by the recent shadows of Simon Russell Beale, Alan Rickman, Alan Cummings, Stephen Dillane, Ralph Fiennes, Mark Rylance, Adrian Lester and Ben Whishaw, but for some of Law’s audience this will be a first, a virgin Hamlet, and not an exercise in comparison by aged critics.

For those not jaded, I reckon it’s worth queueing early in the morning at the Wyndham for one of the 30 tickets released on the day.

The play is directed by Michael Grandage as part of the Donmar Warehouse series in the West End, which included Kenneth Brannagh’s brilliant Ivanov. The Donmar was an early adopter of the famous-folk strategy, more than a decade ago, when Nicole Kidman got nekkid for a thrifty £250 a week in The Blue Room at the Donmar Warehouse. Recently, Ewan McGregor played Iago in Othello there.

Kevin Spacey brought the Hollywood hills to London at the Old Vic, which will be showcasing Ethan Hawke in The Cherry Orchard soon, and the theatre-film crossover is such that now Ian McKellen and Patrick Stewart are performing that well-known Beckett play: Waiting for Gandalf (and the Captain of the Starship Enterprise.) For all but a few, this cultural mash-up is thrilling. It’s likely that Shakespeare would rejoice that we groundlings are fighting for tickets on eBay. Bring on the Hamlet Hunks. Or as Benedict Nightingale of The Times put it: “What next? The Daniel Craig Hamlet?”

Oooh, yes.

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