He was born in Ainsdale in Lancashire and trained at the Royal Academy of Dramatic Art in London. After appearing in Music Hall, he joined the Old Vic in 1932. During the Second World War he was an Army Officer and made one of the area commanders of the auxiliary units . Later he joined the Special Operations Executive and served as a liaison officer with the partisans in Albania (reportedly, his service with the SOE seriously affected him, and he never felt comfortable talking about it). In 1944 he was the aide to the Governor of Gibraltar at the time of the air crash of General Władysław Sikorski's aircraft on July 4, 1944. He described his experiences in a fictionalised form in Eight Hours from England .

From 1948 to 1956 he directed at the Shakespeare Memorial Theatre, and laid the foundations for the creation of the Royal Shakespeare Company. His own Shakespearian roles included Falstaff and Othello; and he also appeared in contemporary plays.

His film roles included parts in Ice Cold in Alex (1958),Tarzan's Greatest Adventure (1959), The Guns of Navarone (1961) and Lawrence of Arabia (1962). He was nominated for an Academy Award for Best Supporting Actor in 1969 for his role in Anne of the Thousand Days.

Television appearances include the title role in the 1969 ITC drama series Strange Report.

Quayle was knighted in 1985 and he died in London from liver cancer in October 1989, aged 76. He was married twice. His first wife was the actress Hermione Hannen (1913-1983) and his widow and second wife was Dorothy Hyson (1915-1997). He and Dorothy had two daughters Jenny and Rosanna.