Having sold out for its entire run until mid-November, with tickets being traded for crazy prices on eBay, this Hamlet faced a tall order in living up to its anticipation as one of Royal Shakespeare Company’s biggest events for years.

Remarkably, it very nearly succeeds. This is among the most gripping and compelling accounts of the play I have seen.

The main reason is that it has a simply electrifying performance from David Tennant in the title role, but this is an outstanding solo performance at the heart of an outstanding ensemble production.

Once again, the Courtyard itself, with its exciting relationship between actors and audience, is one of its stars. That is apparent from the very first scene, where as the sentries fumble in the dark there is a feeling of being right there with them on Elsinore’s battlements which I have never quite experienced before.

There is no getting away from the fact that the title roles in Doctor Who and a Stratford Hamlet are an extraordinary combination, but David Tennant is an actor with the ability to span the distance with what he makes look like ease.

It is often said that David Warner’s Hamlet 40 years ago connected with the 60s generation, and perhaps Tennant is similarly an actor for the times, though I’m not sure what some of his very young fans will make of this.

It’s a freewheeling, some might feel self-indulgent performance of great physical energy which connects strongly with the grim humour of the play.

Tennant takes licence from the fact that Hamlet is himself playing a part, and I thought at first he might be overdoing the mannerisms and funny voices, but his self-assurance is hard to resist.

It’s as though Shakespeare’s words are not so much being delivered as given a thorough work-out: I’ve never heard the lewd insinuation of “country matters” made quite so unmistakable.

Gregory Doran’s production is lean and pacey. Some cuts include Hamlet’s tedious letter about his adventure with the pirates, so it’s anyone’s guess where he’s coming from in the graveyard scene or what happens to Rosencrantz and Guildenstern.

Six chandeliers are lowered to signify the Danish court and dress is modern, so that Tennant does “To be or not to be...” in tee-shirt and jeans on a bare stage, daringly making it look like a rehearsal. The play-within-a-play, by contrast, is given a lavish Elizabethan dressing.

Patrick Stewart doubles the roles of Claudius and the Ghost, pointing up the contrast between Hamlet’s father and his bespectacled, peacemaking brother, who has the air of a benign politician or a philanthropic businessman. It’s an interesting and unusually sympathetic treatment of the character.

Penny Downie is also a more than usually youthful and slinky Gertrude, and this is the first time I’ve heard Hamlet’s squeamish, not to say politically-incorrect, reproach for his mother’s sexuality greeted with an ironic laugh.

Other notable contributions include Oliver Ford Davies’s beautifully conceived Polonius, less querulous than is often the case if no less pedantic, John Woodvine as a resonant Player King and Mark Hadfield, always to be relied on for a good comic turn, as the Gravedigger.

Running time: Three hours, 40 minutes. Until November 15 (returns only).