There's been more anticipation riding on this version of Hamlet starring Andrew Scott than any other since his Sherlock co-star Benedict Cumberbatch gave us his gloomy Dane in a sell-out production last year.

But in the end, both the speculation and the comparisons are rendered almost pointless by a thrilling production directed by Robert Icke that is so bold it just takes the breath away. It is profoundly thoughtful, and yes, Scott is wonderful – but he is the heart of a rich and radical interpretation of the play.

Icke has shaped a lengthy – almost four hours – and unusual version of the text, that includes many sections often omitted. But in doing so he casts light on places usually left unexplored, filling out and re-imagining problematic relationships. It never feels a second too long, gripping from start to close.

On Hildegard Bechtler's simple yet effective set, with glass panels across the rear of an almost empty stage, we first meet Hamlet in the glamorous setting of a party where his mother is smooching indecorously with her new husband Claudius. Shoulders hunched, fiddling obsessively with the watch on his wrist, he is constantly on the verge of tears as he remembers his father the King.

When that father appears to him as a Ghost – via the closed circuit TV screens in Elsinore's corridors and then in person, his first instinct, his most human act, is to hug him. This is a man already almost unhinged by grief. He is also a Prince singularly unready for the act of revenge now demanded of him. 'Am I a coward? is the question that haunts Scott's Prince, sending him on a trajectory that brings him not to acceptance of his role as an action man, but to a numbed acquiescence in his fate. The readiness really is all a good man has left to cling to.

In scene after scene Icke and his cast intelligently rethink the play. In the process they very much make it a play for today not just because Bob Dylan and Laura Marling provide a soundtrack, or because cameras and newsreels form such a part of the action, but because they are prepared to answer the questions Shakespeare sets with a kind of bravura energy and courage.

For example, it is a stroke of genius to try to answer some of the difficult issues around Hamlet's relationship with Ophelia by inventing a silent moment when he cries on her shoulder, and then allowing him to overhear her conversations with her father and brother where they warn her against him. The fact that an ally becomes a potential enemy helps to make sense of their subsequent relationship, an insight underlined by Jessica Brown Findlay's brave performance, which makes Ophelia's frustration heart-breaking; her innocence curdles in front of our eyes and she is powerless to resist.

In the same way, Gertrude's physicial obsession with Claudius – they are in bed when the Norwegian ambassador comes online – explains her reluctance to believe the worst of him. It is only when she realises he is trying to kill her son, that she acts.

Some interventions are audacious: the play scene comes to a juddering halt and sends the audience out into a Brechtian interval as Claudius reveals his guilt in front of the ever-watchful cameras; the ending, which it is a shame to spoil, will have some purists spitting but it is utterly convincing in the emphasis it places on Hamlet's longing for oblivion.

The performances are equally radical, but beautifully pitched. Juliet Stevenson is a wonderfully subtle Gertrude, and her delivery of the news of Ophelia's death has a resonant simplicity; Angus Wright is an urbane Claudius, David Rintoul a regal ghost and a dignified Player King, and Peter Wight an irritating and over-protective Polonius. Even Rosencrantz and Guildenstern, in the hands of Calum Finlay and Amaka Okafor are cleverly and movingly differentiated.

But for all the brilliance around him, it is Scott's night – and he dazzles. His most amazing feat is to make the famous soliloquies acts of intimacy with the audience; you can hear a pin drop as he takes us into his confidence, his thoughts sometimes slow, sometimes racing.

He brings humour and bite to the role, too, turning his advice to the players – its instruction to mimic nature – into a guide for the effect of the production as a whole. In mining all the shifts of Hamlet's character with compassionate understanding he reveals a truly sweet Prince. An outstanding performance on a truly memorable night.

Hamlet runs at the Almeida Theatre until 15 April.