Brambell is the youngest of three sons born to Henry Lytton Brambell, a cashier at the Guinness Brewery, and his wife, Edith Marks, a former opera singer. His first appearance is as a child, entertaining the wounded troops during World War I. Upon leaving school he works part-time as a reporter for The Irish Times and part-time as an actor at the Abbey Theatre before becoming a professional actor for the Gate Theatre. He also does repertory at Swansea, Bristol and Chesterfield. In World War II, he joins the British military forces entertainment organisation Entertainments National Service Association (ENSA).
His television career begins during the 1950s, when he is cast in small roles in three Nigel Kneale/Rudolph Cartier productions for BBC Television, The Quatermass Experiment (1953), Nineteen Eighty-Four (1954), and Quatermass II (1955). All of these roles earn him a reputation for playing old men, though he is only in his forties at the time.
It is this ability to play old men that leads to his casting in his best remembered role, as Albert Steptoe, the irascible father in Steptoe and Son. This begins as a pilot on the BBC’s Comedy Playhouse, and its success leads to a full series being commissioned, running from 1962 to 1974 including a five-year hiatus. There are two feature film spin-offs, a stage show, and an American incarnation entitled Sanford and Son, some episodes of which are almost exact remakes of the original British scripts.
The success of Steptoe and Son makes Brambell a high-profile figure on British television, and earns him the supporting role of Paul McCartney‘s grandfather in The Beatles‘ first film, A Hard Day’s Night (1964). In 1965, Brambell tells the BBC that he does not want to do another series of Steptoe and Son and, in September that year, he goes to New York City to appear in the Broadway musical Kelly at the Broadhurst Theatre, however, it closes after just one performance.
Apart from his role as the older Steptoe, Brambell achieves recognition in many films. His performance in The Terence Davies Trilogy wins him critical acclaim, far greater than any achieved for Steptoe and Son. Although he appears throughout the full 94-minute piece, Brambell does not speak a single word.
After the final series of Steptoe and Son is made in 1974, Brambell has some guest roles in films and on television. He and Harry H. Corbett also undertake a tour of Australia in 1977 in a Steptoe and Son stage show.
Brambell dies of cancer in Westminster, London, on January 18, 1985, at the age of 72. He is cremated on January 25, 1985 at Streatham Park Cemetery, where his ashes are scattered.