Howard Brenton’s meaty new history play, set during the final 55 days in the life of Charles I, brings to mind a very modern problem.

In 1974 you could tell a Labour politician from a Tory by the suit he or (less often) she wore.

Or as Labour’s chief whip says in James Graham’s new play, you can tell by the shoes visible under the doors of the Commons toilet cubicles — all the better to flush MPs out before a crucial vote.

When in 1833 Edmund Kean, the greatest actor of his generation, collapsed on stage while playing Othello at Covent Garden’s Theatre Royal, the theatre’s manager risked public outrage by hiring an African-American called Ira Aldridge – terrifically played here by Adrian Lester – to step into Kean’s shoes.

You might say that the National Theatre has done for Howard Barker what, in Barker's play, the Doge of Venice does for the 16th-century female artist, Galactia.

Anton Chekhov’s masterpiece has been reworked before, and with rewarding results. In 2008, a version by Diane Samuels and Tracy-Ann Oberman set the play in post-war Jewish Liverpool. Instead of yearning to see Moscow, the siblings were in a New York state of mind. And instead of Olga, Masha and Irina, we had Gertie, May and Rita.

It had long been on the cards that Sheridan Smith would complete the transition from frothy TV sitcom to the classical stage. On the way she delivered acclaimed performances, such as her Olivier-winning Elle Woods in the musical Legally Blonde and a cameo as a lonely wife in Flare Path.

There has probably never been a play quite like it. In almost two uninterrupted hours this new offering by Caryl Churchill propels us through countless short, seemingly unconnected conversations. There is no plot, no setting — but for the giant white cube in which each conversation takes place — and for much of the time the play does not make much sense.

Did Lear sexually abuse his daughters? In Michael Attenborough’s austere new Shakespeare production, with a splendidly bearded Jonathan Pryce in the title role, there is more than a hint of something dark and inappropriate in Lear’s family history.