He was educated at the private Abberley Hall School and Rugby School and trained at the Royal Academy of Dramatic Art in London. After appearing in music hall, he joined the Old Vic in 1932. During World War II, he was a British Army officer and was made one of the area commanders of the Auxiliary Units in Northumberland.

Quayle made his Broadway debut in The Country Wife in 1936. Thirty-four years later, he won critical acclaim for his starring role in the highly successful Anthony Shaffer play Sleuth, which earned him a Drama Desk Award.

His first film role was a brief uncredited one as an Italian wigmaker in the 1938 Pygmalion – subsequent film roles included parts in Alfred Hitchcock's The Wrong Man, Michael Powell and Emeric Pressburger's The Battle of the River Plate (both 1956), Ice Cold in Alex (1958), Tarzan's Greatest Adventure (1959), The Guns of Navarone (1961), H.M.S. Defiant, David Lean's Lawrence of Arabia (both 1962) and The Fall of the Roman Empire (1964). He was nominated for an Academy Award for Best Supporting Actor in 1969 for his role as Cardinal Wolsey in Anne of the Thousand Days.

He was an aide to the Governor of Gibraltar at the time of the air crash of General Władysław Sikorski's aircraft on 4 July 1943. He fictionalised his Gibraltar experience in his second novel On Such a Night, published by Heinemann.

From 1948 to 1956 Quayle directed at the Shakespeare Memorial Theatre, and laid the foundations for the creation of the Royal Shakespeare Company. His own Shakespearian roles included Falstaff, Othello, Benedick in Much Ado About Nothing, Henry VIII and Aaron in Titus Andronicus opposite Laurence Olivier; he played Mosca in Ben Jonson's Volpone; and he also appeared in contemporary plays. He played the role of Moses in Christopher Fry's play The Firstborn, in a production starring opposite Katharine Cornell. He also made an LP with Cornell, in which he played the role of poet Robert Browning in The Barretts of Wimpole Street.

Television appearances include the Armchair Theatre episode "The Scent of Fear" (1959) for ITV, the title role in the 1969 ITC drama series Strange Report and as French General Villers in the 1988 miniseries adaptation of The Bourne Identity. He starred in the 1981 miniseries Masada as Rubrius Gallius. Also he narrated the miniseries The Six Wives of Henry VIII in 1970, and the acclaimed aviation documentary series Reaching for the Skies.

In 1984 he founded Compass Theatre Company, which he inaugurated with a tour of The Clandestine Marriage, directing and playing the part of Lord Ogleby. This production had a run at the Albery Theatre, London. With the same company subsequently toured with a number of other plays, including Saint Joan, Dandy Dick and King Lear with Quayle in the title role.

Quayle was appointed a Commander of the Order of the British Empire (CBE) in the 1952 Birthday Honours and knighted in the 1985 New Year Honours for services to the Theatre. He died at his home in Chelsea from liver cancer on 20 October 1989. He was married twice. His first wife was Actress Hermione Hannen (1913–1983); his second wife and widow was Dorothy Hyson (1914–1996), known as "Dot" to family and friends. He and Dorothy had two daughters, Jenny and Rosanna, and a son, Christopher.