It is unusual for a new production of Hamlet to be a front-page news story. It is remarkable when the actor playing him is not a film or television star, but a jobbing actor in his early thirties. The critical recognition of Rory Kinnear's Hamlet is about the most cheering thing to happen to the arts since rumours of the scale of the projected cuts took hold.

In a way, this traditional, text-based National Theatre production is radical. It has become convention that Hamlet should be a television or film star. I went to the first night of Jude Law's Hamlet, which resembled a red carpet film premiere.The paparazzi were lined up by Leicester Square, the audience was starry. It was a fine production by Michael Grandage, the talented, departing artistic director of the Donmar Theatre, and Jude Law was an athletic and cool Hamlet. But it did not add much to my understanding of the play.

Last Wednesday at the National, by contrast, I was reminded of the Ambrose Bierce saying: "There is nothing new under the sun but there are lots of old things we don't know." Rory Kinnear looks like a young Clive Anderson. The only television part I have seen him in was playing Denis Thatcher, to Andrea Riseborough's Margaret, in The Long Watch to Finchley (both of them superb). He lacks the glamour of Jude Law or David Tennant or the heartbreaking quality of Ben Wishaw. What he has instead is the powerful gift of trained intelligence. I do not mean that most actors are stupid, but being light on thinking is not a deal breaker. Emotional intuition will do fine.

Rory Kinnear went to the same school as George Osborne and the same Oxford college as Yvette Cooper, and it shows. The Independent on Sunday theatre critic pays tribute to his "penetratingly intelligent" Hamlet. Kinnear and the director Nicholas Hytner are both concerned by clarity and lucidity in meaning. In the programme notes, Hytner talks of Hamlet's search for "authenticity" in a world of distrust and duplicity. As we left the theatre at the end of an uncompromising three hours 45 minutes, a literary critic said to me excitedly that he had heard every word Kinnear had said. I replied that, even better, I had understood every word.

Until this Hamlet, I was never sure how much the madness was feigned or what Hamlet really felt towards Ophelia. Many of the lines were so famous they had lost their meaning. Kinnear went for the full rebirth of Shakespeare. And it takes, I think, a British theatre actor, to do this. All the "fresh perspectives" on Shakespeare, from American actors or power crazed designers, can take you further away from the plays.

Hytner's Hamlet is set in modern times but its design flourishes accentuate the play rather than distract from it. Could it be that Hytner can take the risk of a non-starry rediscovery of Shakespeare because his neck is not on the block at the National Theatre, and he is not always fretting over where the next funding will come from?

I am general sympathetic towards Con-Lib cuts, but I fear the slashing of arts funding is a short-sighted degradation of the nation's cultural life. The arts have replaced manufacturing as something we do very well and which cannot be outsourced to India. I hope Jeremy Hunt will be baptised into an understanding of this by a visit to Kinnear's Hamlet.

Sarah Sands is deputy editor of the London Evening Standard