Born in Berkshire, Price enjoyed a long and successful film career, the high point of which was his performance as the suave murderer in the British comedy classic, Kind Hearts and Coronets (1949). His first starring part was in A Canterbury Tale in 1944, and he went on to appear in dozens of British films.
In 1965, he became popular with television audiences for his performance as Jeeves opposite Ian Carmichael as Bertie Wooster in The World of Wooster. His premature death was caused by cirrhosis of the liver.