At the conclusion of a year in which Britishness has come so resoundingly to the fore of the national debate – and with a play that at the time of its writing, 1605-6, was engaging with that concept no less urgently – the first impression made by Gregory Doran’s King Lear is how far removed it looks from any traditional sense of "British".

David Troughton (b.1950), a familiar face on television and a Royal Shakespeare Company veteran, is a versatile actor. His most recent RSC appearance before Gloucester displayed his talent for comedy: he was a funny and energetic Simon Eyre in Dekker's The Shoemaker's Holiday in his favourite theatre, the Swan at Stratford. Previous roles for the company have included Kent in an earlier Lear with John Wood as the king, Bolingbrooke in Richard II and the title roles in Richard III and Henry IV, parts 1 and 2.

“Britain is a world by itself.” It could be the slogan of the year – and rather longer, probably – but the phrase comes from Shakespeare’s late romance Cymbeline. Its Act III scene, in which Britain announces that it is breaking its allegiances to the Roman Empire, surely can’t ever have played before with quite the nuance that Melly Still’s RSC production gives it. It premiered at Stratford in May, when the big Brexit question was still open, and now reaches the Barbican with redoubled relevance.

The confidence trick to end all tricks, Ben Jonson’s The Alchemist is so utterly recognisable, so clearly contemporary, that to update the setting feels a bit like underlining the point in red pen. In this transfer from Stratford's Swan Theatre director Polly Findlay plays things 17th-century straight, allowing her audience to make the connection with just a little help from an irreverent new epilogue.

What price a human soul? That’s the question Marlowe’s Doctor Faustus asks – a question whose answers are rooted in faith and theology. But in a society with little use for faith and still less for theology, how do you reframe the question? Director Maria Aberg offers a deft if not always entirely coherent answer in her breathless, punky take on the play for the RSC.

Pro patria mori. Now there’s the test for Henry V - perform it on Remembrance Day. The “band of brothers” shtick relies on an idea of patriotism from an age when there was no need to define something so heartfelt, and an idea that kings and commoners were all in it together when fighting the enemy. After all, Henry orders the good English soldiers to rape French girls, smash the heads of French grandfathers, and skewer their babies on pikes, no questions asked. The bonuses of patriotism, if you like.

Jane Lapotaire's distinguished career on stage and screen was cut short in 2000 when she collapsed in Paris with a massive brain haemorrhage. She was giving a Shakespeare masterclass at the time and now, 15 years later, at the age of 70, she is once again acting on stage in Shakespeare.

We’re so used these days to theatre music as aural torture – blasts of pop music on the tannoy, assorted electronics or, if you’re (moderately) lucky, a snatch of too-loud Chopin or Grieg before the lights come up on the Ibsen drawing-room – that it’s easy to forget a time when plays were introduced, interrupted and even accompanied by a pit orchestra playing music specially composed by the greatest composers of the day. We now hear this music as concert overtures and suites: Egmont, Peer Gynt, L’Arlésienne, and the like.

Roger Rees, whose death at the age of 71 was announced yesterday, never intended to act. He trained at the Slade and made extra money painting theatrical scenery. One day a director asked if he’d like to act, and he laid down his brush. The second time he applied to join the RSC, he got in. He stayed with the company for a now unimaginable 22 years and in due course became one of the great stars of British theatre in the 1980s.

We’ve not been short of memorable London productions of Arthur Miller’s best known works. Ivo van Hove’s triple Olivier award-winning A View from the Bridge, which transferred to the Wyndham’s Theatre from the Young Vic earlier this year, and the Old Vic’s The Crucible, directed last year by Yaël Farber, were two exceptional productions. And now we have the seminal play of the 20^th century. The RSC’s Death of a Salesman arrives from its short run at Stratford garlanded with plaudits, but it’s even better in this West End transfer.