What a time to be the Almeida Theatre. Under Rupert Goold, the north London powerhouse is impressively and consistently solid, either at its base in Islington or in its West End transfer. Most other theatres can but look on and wonder just how they do it. King Charles III, now at the Wyndham’s Theatre, is possibly the best of a brilliant bunch.

I didn’t get a chance to catch King Charles III when it was first on, and so took my seat with just a vague understanding of the plot (something about the brief future reign of Prince Charles following the death of our current monarch), yet not of its form or style. Mike Bartlett’s writing is as clever as it is engrossing. Bartlett displays a masterful grasp of the iambic pentameter, writing fresh, clean (and most importantly, penetrable) Shakespearian verse, paying homage to the bard and his work through witty, subtle and unexpected references to well-known Shakespearian characters and scenes. This heightens the tension, the drama, and ultimately the tragedy, and is the first contemporary play I’ve ever seen that makes me wish I had a firmer grasp of Shakespeare.

Lines such as “our king is mad” or “a politician’s tongue you have indeed” could quite clearly be plucked from King Lear (as could stormy final scenes and Charles’ physical descent into chaos), while the inclusion of the ghost of Diana is almost Hamlet-esque. Another notable mention could be Kate and Wills’ Macbeth-style betrayal and treachery. There’s plenty to choose from here. For Shakespeare buffs these will be a delight. For everyone else, the entire production is so strong that any lost references really don’t matter.

Tom Scutt’s design fits beautifully. A distressed brickwork backdrop lends itself well to the spectacle and grandeur of the palace and Westminster, yet also appears crumbly enough around the seams to display a country in a state of turmoil, of panic on the streets of London. Paul Arditti’s searing score creates and sustains a chilling yet rousing undercurrent, especially at the very end, where we are reminded just how well the British do pomp and ceremony.

And then there are the performances. With or without the look-a-like/sound-a-like elements (which do exist), the entire company is hugely impressive. Lydia Wilson is endearing as Kate, lamenting the dearth of women in power; Oliver Chris, fresh out of the other important contemporary play on now (Great Britain), is suitably angsty as William; and Adam James, Nicholas Rowe and Miles Richardson are riveting as the politicians and press officers trying to keep their heads above water. Tim Pigott-Smith is enthralling as his namesake. He is noble and resilient, yet fragile and vulnerable and creates a tragic figure of which Shakespeare would be proud. King Charles III is majestic.

King Charles III is on at the Wyndham’s Theatre until 29 November. For more information and tickets, see the Almeida Theatre website.