Sir Antony Sher, one of British theatre’s most acclaimed and respected stage actors, has died of cancer at the age of 72. His terminal illness was revealed in September, when the Royal Shakespeare company announced that its artistic director, Sher’s husband Gregory Doran, would be taking compassionate leave to care for him.

Sher’s death was announced on Friday. Catherine Mallyon, RSC executive director and Erica Whyman, acting artistic director, said: “We are deeply saddened by this news and our thoughts and sincere condolences are with Greg, and with Antony’s family and their friends at this devastating time. Antony had a long association with the RSC and a hugely celebrated career on stage and screen.”

It is his vivid performances in productions over four decades with the RSC, many of them directed by Doran, which gained Sher his reputation as one of the great modern Shakespearean actors. In 1985 he won the Olivier award for a portrayal of Richard III on crutches, his image a striking realisation of the character’s description in the play as a “bottled spider”. For the same director, Bill Alexander, he played Shylock in The Merchant of Venice. Doran directed him as Macbeth and King Lear, and as Falstaff in Henry IV Parts I and II, and Iago in Othello. As Lear, performed between 2016 and 2018, he was praised as “unbearably moving” by the Guardian’s Michael Billington.

Sher played another great Shakespearean, Edmund Kean, in Sartre’s bio-drama Kean directed by Adrian Noble. But his range went well beyond the Bard. The 1985 Olivier award was given to him in honour of both his Richard III and his performance as a drag queen in Harvey Fierstein’s Torch Song Trilogy, enabling him to say in his acceptance speech: “I’m very happy to be the first actor to win an award for playing both a king and a queen.”

He was praised for his Cyrano de Bergerac and his Willy Loman in Death of a Salesman, both with Doran and the RSC. He excelled as both Tartuffe and that play’s author, Molière (in a play by Bulgakov) in RSC shows. Lead roles as Brecht’s Arturo Ui and Kafka’s Joseph K came at the National Theatre. The real-life figures he portrayed included Freud in Terry Johnson’s play Hysteria at the Theatre Royal Bath and Primo Levi, both at the National Theatre (in a play Sher wrote himself) and on screen too.

Sher was born in 1949 in Cape Town, where his grandparents had moved after fleeing the Lithuanian pogroms. He revisited their journey in his novel Middlepost and returned to South Africa during his career with major theatre productions including The Tempest (playing Prospero), Titus Andronicus (in the title role) and Arthur Miller’s Broken Glass, whose hero, said Sher, was as “uncomfortable in his own skin” as the actor himself.

He grew up fascinated by the performances of great Shakespearean actors – obsessively listening to an LP of Laurence Olivier’s Othello – and his understanding of drama was transformed by the plays of Harold Pinter. He arrived in London in 1968, at the age of 19. “I looked around me and I didn’t see any Jewish leading men in the classical theatre, so I thought it best to conceal my Jewishness,” he once said. “Also, I quickly became conscious of apartheid when I arrived here, and I didn’t want to be known as a white South African.” He concealed his sexuality in public, too, which meant “my entire identity was in the closet”.

Sher prepared one of Mick’s speeches from Pinter’s The Caretaker for his drama school tryouts but at his Rada audition “they urged me to seek a different career”. He studied instead with the Webber Douglas Academy of Dramatic Art and gained early stage experience with the group Gay Sweatshop and at the Liverpool Everyman, playing Ringo in Willy Russell’s John, Paul, George, Ringo … and Bert.

While Sher’s principal commitment was to the stage, he could be seen regularly on TV (including in the series The History Man) and in films. He wrote plays and novels, the memoir Beside Myself and autobiographical accounts of some of his best known performances, including as Richard III and Falstaff, which opened up the craft of acting. Year of the Mad King: The King Lear Diaries won the Theatre Book prize in 2019. It featured a number of his own illustrations and Sher remained a passionate painter. He was knighted in 2000 for his services to the arts.

Sher and Doran entered into civil partnership on the first possible day of the new law, 21 December 2005, which he called “a great day for human rights”. The couple married in 2015.

His final roles on stage included that of a chilling torturer in Pinter’s One for the Road in the Pinter West End season, and in John Kani’s play Kunene and the King, which premiered in the Swan theatre, Stratford-upon-Avon, in 2019, directed by Janice Honeyman. Its London run was curtailed by the first lockdown.

Sher’s love for language was always palpable in his performances. “To an actor, dialogue is like food,” he wrote in Year of the Fat Knight, his book about Falstaff. “You hold it in your mouth, you taste it. If it’s good dialogue the taste will be distinctive. If it’s Shakespeare dialogue, the taste will be Michelin-starred. Falstaff’s dialogue is immediately delicious: you’re munching on a very rich pudding indeed, savoury rather than sweet, probably not good for your health, but irresistible.”

• This article was amended on 3 December 2021 to clarify that Doran directed Sher as Iago in Othello.