Known for his roles as Jerry Leadbetter and Jim Hacker on the respective BBC television series The Good Life and Yes Minister, Eddington is also remembered for his performances in the films The Devil Rides Out and The Amazing Mr. Blunden. He began his career during the World War II years, performing with the Entertainments National Service Association. He went on to act with a Sheffield theater company and to appear in the 1950s television series The Adventures of Robin Hood.
