"King John". Jesus College Shakespeare Project.

If Shakespeare’s works were a huge mansion, and each play a room in it, Romeo and Juliet might be the Grand Ballroom, Hamlet the Old Library, and A Midsummer Night’s Dream the Parkland Walk on a warm, Trinity-term evening.

King John would be somewhere in the East Wing. No one goes there very often. It’s dark and unfamiliar, and it smells of death. It's not often opened up nowadays.

But on the basis of tonight's show, it undoubtedly should be. The Jesus College Shakespeare Project reveals King John to be not just a thrilling watch, replete with betrayal, murder, battles and unexpected twists, but also stylistically and thematically in step with our own cynical age.

The Victorians loved this play (but then, they loved going to freak shows and subjugating entire foreign nations too, so they didn't always get it right). It was so popular at the end of the 19th Century that in 1899 it became the first Shakespeare play to be made into a film - silent, four minutes long, and effectively a trailer for Herbert Beerbohm Tree's ultra-naturalistic stage version that was wowing West End visitors at the time. To us, the spectacle of a hopeless, mendacious, self-obsessed leader is so familiar that this play looks almost like contemporary satire. For the Victorians, bestriding the world like colossi under the protective bustle of their goddess-empress, it must have been like a warning from history.

As ever, the Jesus College company members deliver their lines with a degree of clarity, pace and perception that would leave many a professional troupe blushing. From the humblest messenger to the lead role, the verse-speaking is so immaculate that it makes you realise why experts go on about it so much. Basically, if you do it right, everyone can understand what you're talking about, and these actors do it so right. I've been in the East Wing of King John on a few previous occasions, but I never really got the point of it until this evening.

On top of that clarity, this production recognises and excavates the rich seam of cynicism that lies below the surface of this play. From the very start, the facial expression that imprints itself on the audience's eyes is a joyless, insincere rictus. Every character smiles, whether threatening war or (worse) marriage. Director Peter Sutton brings out the machinations that churn behind the platitudes merely by having the characters be polite to each other. It's like Succession with ruffs.

And the truth is, like Succession, and with the possible exception of an innocent ten-year-old boy, there is no one likable in King John. Everyone is viciously self-serving and constantly on the lookout for a way not only to beat their opponents but to be really nasty to them at the same time. John himself is played to preeningly pompous perfection by Alex Still, who, after his versatile roles in Henry VI, Richard III and Titus Andronicus, must surely be one of the outstanding Shakespearean actors currently at this university. His nemesis King Philip of France (Roman Pitman) is like a smiling, dormant crocodile, waiting for the moment to pounce. The offhand way in which they agree to collaborate in murdering all the inhabitants of Angiers before resuming their own disagreement is so chilling that, even with the Northern Lights setting the sky afire outside, my blood ran cold.

A directorial concept to set the play in both the reigns of Elizabeth the First and Second simultaneously sounds excitingly experimental in the programme notes, but doesn't quite take flight in performance. The modern and Elizabethan elements are not clearly delineated other than by minor costume differences, and the satirical point of the comparison does get slightly lost in the complications of the play itself. But this is no bad thing. In fact, it releases the play to do its dirty work for itself. John, for example, although intentionally dressed as a frumpy Virgin Queen Gloriana, actually looks and behaves more like an eighteenth-century fop, complete with white make-up and extravagant wig, like a minor nobleman from Blackadder III - and it's an ideal touchstone for his character.

What's not mentioned in the programme notes is the other major link that modern audiences have with the historical King John. And that is of course A.A. Milne's wonderful children's poem King John's Christmas (first published in Now We Are Six, 1927). Although Milne's John doesn't have any nephews murdered, he does have the same childish petulance as Shakespeare's original, and his presence is palpable in this production.

Milne had one foot in the 19th century, and he knew what attracted the public to King John. It was his fragility; his pathetic need for approval; his childish desires. He was a figure of fun, but also a reminder that there's a damaged human at the heart of that ridiculous, self-regarding pomp. All he wanted for Christmas was a big, red, India-rubber ball. And this production, quite brilliantly and understatedly, gives him one, elegantly connecting Milne and Shakespeare, but also underlining the egotistical affectation of John by having him bounce that ball obsessively, like a Bond villain stroking a cat.

It's a subtle but superbly eloquent way not only to make the connection with Milne's poem, but also to show the ineptitude of leaders who allow their personal obsessions to override their civic responsibilities. And the Milne theme of Kings as children is continued in Pitman's King Philip, who bounces off the walls in frustration like a Disney cartoon.

Between these two toy puppets, Ollie Gillam as the Bastard Philip Falconbridge is a superb puppet-master. Charming, warlike and out for himself, he feels like a study for Henry Hotspur, due to emerge a couple of years later in Henry IV.

Working chronologically, this is the third play in a row where Shakespeare has had a central character the audience simply can't root for. At least Richard of Gloucester was fun, and part of the genius of Richard III is the pantomime villain appeal. But still, he's no hero. Titus from Titus Andronicus is a child-executing fundamentalist. And now here's John, a king with fewer redeeming features than Vladimir Putin. But don't worry. The bad guys are finished for now, and the gentle uplands of comedy and romance are just around the corner, with Love's Labour's Lost coming in Michaelmas. I don't know about you, but based on this production, I can't wait.