Born in London’s south-east district of Peckham, the son of Sarah Ann O’Leary and William Burke, he was educated at Leo Street Boys’ School and Walworth Central School. Burke started work aged 14, working in a railway repair firm in the City of London after leaving school. He became a club steward and also worked in a silk warehouse, joining a local amateur dramatics group before moving to Morley College and winning a scholarship to RADA in 1937. His acting career started two years later at the Barn Theatre in Shere, Surrey. His budding career was interrupted by the Second World War, when he registered as a conscientious objector, and was directed to work on the land.

In the late 1940s, he worked with the Young and Old Vic and other companies. His London debut was in 1950 at the Watergate Theatre, appearing in Pablo Picasso’s play Desire Caught by the Tail. He then spent three years with Birmingham Repertory Theatre (1950–53) and appeared in the 1954 West End hit Sailor Beware!.

On stage Burke appeared in several productions by the Royal Shakespeare Company, including Richard II, Romeo and Juliet, Roberto Zucco, The Tempest, Peer Gynt, Measure for Measure, Troilus and Cressida, Two Shakespearean Actors, All’s Well That Ends Well and Antony and Cleopatra. In 2008 he appeared at the National Theatre as the Shepherd in a new version of Sophocles’ Oedipus by Frank McGuinness.

Burke died from a chest infection on 16 February 2011, twelve days before his 93rd birthday, and was cremated at Golders Green Crematorium. He was survived by his wife, Barbara (née Bonelle) and their four children: Jacob and Harriet (twins), and Kelly and Louisa (twins).