When the distinguished Jewish lawyer Sir Sydney Kentridge, once Nelson Mandela’s defence counsel, moved to London in the 1990s, his eldest son William decided to stay in South Africa to make protest art — and was overlooked by critics for decades as a result.

Now the man who has been celebrated as one of the world’s greatest living artists is finally gaining recognition in London with a significant retrospective at the Royal Academy (RA).

Drawing for Projection-William Kentridge

Kentridge's Drawing for Tide Table (2003)

It’s a dramatic show that has impressed critics with the astonishing variety of media through which Kentridge tells his stories. They range from bronze sculptures to puppet theatres, animated films and gigantic tapestries, all based on drawings which, like their subject matter, seem larger than life.

Like his parents — his late mother, Felicia Geffen, was an anti-apartheid activist — Kentridge rages against the world’s unjust regimes. But he is too cynical to expect a better world in his lifetime.

He is angry about inequality in Africa and the world at large, and was even angry at Lithuania, the most recent state to honour him.

Having resolved never to set foot in the country where his ancestors were murdered, he unexpectedly relented earlier this year, visiting Kaunas to open an exhibition of his work that is the centrepiece of the city’s European Capital of Culture celebrations.

Kentridge’s art is not for the faint-hearted: the RA’s august galleries are now hung with his images of gallows, cupboards of severed heads, grave-studded landscapes and eyeballs — the stuff of nightmares that have infused his work for more than 40 years.

Perhaps that’s why, when he’s not depicting the sins of bourgeois white South Africans at play in his satirical triptych The Conservationist’s Ball or drawing boatloads of migrants, replicated for the RA on some of the largest tapestries ever woven, Kentridge finds relief by inking exquisite flowers and trees as tall as the gallery walls.

1

Migrant Tapestry by William Kentridge

He has made 11 animated films featuring semi-autobiographical characters Soho Eckstein and artist Felix Teitelbaum, Eckstein’s rival in love. Eckstein is a gross, callous industrialist, inspiring the Board of Deputies to call Kentridge’s work antisemitic when some of the films were shown at London’s Serpentine Gallery in 1999.

But that did not stop the Israel Museum inviting him to exhibit following two solo shows in Tel Aviv. In 2012, Kentridge travelled to Israel to accept the Dan David Prize, resisting entreaties not to go.

“I am very aware of the general calls to boycott Israel, and the personal appeals asking me not to come here,” he told Ha’aretz. “I chose not to agree with these calls. Even though the show is not about Jewishness, it raises questions relevant to a Jewish background, questions about historical memory and historical forgetting.”

He admitted, however, that he found the religious extremism and racial intolerance he says he encountered in Israel offensive, and joined demonstrations in east Jerusalem.

The five films on show at the RA are thoroughly engaging, though the stories they tell are sad, mad and often deeply pessimistic. A Magen David appears in one, on the back of a follower of African Zionism wading towards her baptism, a rare example of Kentridge harnessing Jewish iconography.

Kentridge studied theatre and mime in Paris after graduating in political science and art in South Africa, and has seen his opera designs staged at La Scala and the Met as well as the English National Opera. In the final gallery, a spectacular, multi-media production re-creates the myth of the Sybil, the seer who acted as a bridge between the living and the dead.

Some of her predictions are scary — “the execution site is never empty”, reads one — while others are philosophical, even hopeful: “You will for 20 minutes have great happiness. It is not enough. But it is not nothing.”

In the gift shop, the coffee pots, cups and saucers that recur in his work have been metamorphosed into items for sale.

It does not seem tongue-in-cheek, unlike the perfume he has created with Floris to evoke “the comforting dustiness of old books, the fountain gurgling outside the studio door, a crisply pressed white cotton shirt and wooden plan chests laden with prints and drawings”. Is he having a laugh? Kentridge’s black humour pervades even the most brutal of his works.

‘William Kentridge’ is showing at the Royal Academy until 11 December