King Charles III, Wyndham's Theatre

Prince Charles’s “black spider letters” - his attempts to influence or change government policy - are real, as is the government’s long collusion with Clarence House to keep them from the public, despite the efforts of The Guardian in particular to expose them. This gives Mike Bartlett’s play King Charles III, an imagining of the next king becoming a champion of press freedom, a sharply ironic edge deep below its already very entertaining satire.

Transferred from the Almeida Theatre to become, surely, a West End hit, this features among many reasons for enjoyment a magnetic central performance by Tim Pigott-Smith as the sexagenarian prince who is destined for the record books as the oldest Prince of Wales ever to become king. By which time, as he says, “What am I?” He has been so long denied permission to make any decisions that he has no idea how to do it. Straightaway he blunders.

Charles’s wish to assert the “meaning” of being King in a head-on clash with democracy and Parliament is the seriously interesting bit. The delivery of the clash is the fun: however unlikely it might be (given the gruesome revelations of the "tampon" phone calls and Princess Diana’s emulsive media presence), the new monarch wants to defend media freedom against Parliament’s move to pass a draconian law restricting press intrusion into privacy. This charmingly improbable scenario is decorated further with Prince Harry’s infatuation with a Muslim-sympathising art student who’s unfortunately texted a previous boyfriend photos of her intimate parts that are now plastering the tabloids.

Kate calls Prince William 'husband', like a modern Lady Macbeth, and comes nearest to filling the role of villain

Then there are the ghost of Diana, the power-hungry Kate Middleton, the big-hearted mama Camilla, and the slimy Opposition leader. Bartlett works these winningly Shakespearean cartoons into a cunning pastiche of a history play, the royals speaking in blank verse, with some splendid exit lines. Charles soliloquizes: “The Queen is dead. Long live the King… That’s me!” Prince Harry, dazed with delight at what the real world holds, relates iambically: “We went to Sainsbury’s, and shopped for stuff.” And later on exits with: “I’ll go and find a greasy spoon.” Kate calls Prince William “husband”, like a modern Lady Macbeth, and comes nearest to filling the role of villain, taking the decisive action to force two irreconcilables down the unprecedented path of divorce.

The Spitting Imagery is kept just enough at bay by the thought in the writing. The playwright is roughly Prince William’s age; he evidently feels anxiety, under the jokes, at the potential conflagration looming when a media-conditioned public is bereft of a monumental Queen whose associations have almost all been of historically safe distance, and now is presented with the quirky successor who has indulged himself with such damagingly public consequences. (Pictured left, Charles, Prime Minister Evans, William and Harry at the Queen's funeral.) Timely references are made to phone-hacking, current turbulence about Scotland, a new Royal baby, and sexism concerning the Duchess of Cambridge (this last is nice, referring obliquely to Hilary Mantel, whose Wolf Hall plays a step away at the Aldwych also probe the never-absent inconsistencies in what the monarchy is for).

Yet we still come back to basics: can the King dissolve Parliament, just like that? Apparently, yes. And if he did, would Prince William and Parliament ally to force him to abdicate? Reasonably, they might. And would the right reasons have been invoked? Serious ones, not just media demands for a younger face? It's never been tested before. And who is judging? The scribes of history? The Twittersphere?

Rupert Goold stages Bartlett’s play in a forbidding brick chamber perhaps under the Tower of London (set by Tom Scutt), lit with church candles and echoing with Jocelyn Pook's mood-music. It makes emphatically theatrical contrast with the Victorian curlicues of the Wyndham. The cast, some playing several parts, also act as a singing chorus, adding the subtext of the religious imperatives and historical continuity within the monarchy. I like how this sense of visible durability is challenged by the casually contemporary performances (again, Shakespearean).

Prince Harry, portrayed in his raucous Las Vegas stage, is played by Richard Goulding as a rumpled young ass with shades of both Prince Hal and Boris Johnson (right, Goulding with Tafline Steen as Jess). Oliver Chris of Breathless applies a remarkable physical resemblance to the straighter role of William, and counters Harry’s superficiality with a telling reminiscence of his grandmother’s lessons to him about rule: these chime with the Blairish Prime Minister of Adam James, who berates Charles that his mother, over 60 years, had had to sign all sorts of acts she privately may have loathed.

And there is the jewel in the crown: Pigott-Smith, whose pompous but pathetic Charles dithers masterfully somewhere between Nicholas Parsons and King Lear. In the height of his delusion about kingship, he describes democracy as, historically, "an option, added on - like satnav." And when satnav fails, the old-fashioned map never does, he says triumphantly. The final scenes are both emotionally moving and also petty, which strikes me as a perceptive forecast of reality.