Having played Sherlock Holmes’s politically involved older brother Mycroft in the BBC’s hit crime series Sherlock, Mark Gatiss may not be an obvious candidate to now follow in the footsteps of the famous detective. But with his new murder mystery series Bookish, set in London in the aftermath of World War Two, the creator, writer and star of the six-part show has finally become a sleuth himself.

As a sometime writer of Poirot, Sherlock and Christmas ghost stories, Mark Gatiss is no stranger to enigmatic crimes and bizarre occurrences set in carefully-recreated versions of the past. He revisits similar themes in Bookish, his new series about a second-hand bookseller in post-World War Two London who is evidently concealing some hidden depths.

A glamorous black woman sits in a Forties bar under a Vichy cop’s gaze, cigarette tilted at an angle, till two male companions join her in clandestine conversation. The woman is Suzanne Césaire (Zita Hanrot), an influential Martinican journalist and essayist on Surrealism, feminism, Négritude (Francophone black consciousness) and an anti-colonial philosophy honed to a dangerous edge by the Fascist-aligned authorities. More intriguingly for director Madeleine Hunt-Ehrlich, following this feverishly productive period, Césaire never published another word.

The National Health Service was established 77 years ago this month. Resident doctors are about to strike for more pay, long waiting lists for hospital treatment and the scarcity of GP appointments continue to dog political conversation, while the need for reform of the system provides a constant background hum.

Tate Britain is currently offering two exhibitions for the price of one. Other than being on the same bill, Edward Burra and Ithell Colquhoun having nothing in common other than being born a year apart and being oddballs – in very different ways. And since both reward focused attention, this makes for a rather exhausting outing – I’m reviewing them separately – so gird your loins.

“It is so disgraceful, what happened there,” says Anita Lasker-Wallfisch, in a comment that is the understatement of the century. She is referring to the genocide perpetrated by the Nazis in concentration camps like Auschwitz-Birkenau, where she was held prisoner.

There used to be an unwritten rule among BBC commissioners about how long an interval had to pass before greenlighting a new documentary on a familiar subject – Shakespeare, Ancient Egypt, Andy Warhol – they all came round again with a decent interlude between reassessments. But if the pitch involved Nazis, all bets were off. And maybe in Germany itself, that’s been the case with film-maker Leni Riefenstahl who may have had more documentaries made about her than she made herself during her years as Hitler’s favourite director.

When Yasmina Reza’s cerebral play Art arrived in London in 1996, we applauded it as a comedy. Now another French hit, Jean-Philippe Daguerre’s Adieu Monsieur Haffmann, has landed, and the genre confusions could start all over again.

Kurosawa’s 1949 thriller probes post-war morality in a Tokyo whose ruins and US occupation mostly remain just out of shot, in a heatwave causing mistakes and madness. The theft of callow detective Murakami (Toshiro Mifune)’s police pistol on a crowded trolleybus and his guilty hunt for what becomes a murder weapon provide the narrative, and sharp-featured young Mifune’s coiled performance, alternating mimed grace with feline fierceness, is the arrow carrying it to its bruising conclusion.