He was born in Liverpool, England, and began his stage career at the Hippodrome Theatre in Bolton, Lancashire. After a series of bit parts in British films, he made his name as the Reverend Mervyn Noote in the British sitcom, All Gas and Gaiters (1966), which was considered rather controversial because the main characters were senior churchmen (the Bishop, his chaplain Noote, and the archdeacon) who got into various scrapes as a result of their general incompetence.
By the time the series finished, Nimmo was so closely associated with the clergy in the minds of the audience that he went on to play a bungling monk in another BBC sitcom, Oh, Brother. Despite abandoning the upper-class accent for this role, he continued to be offered parts as clergymen and aristocrats. He starred in the West End musical, Charlie Girl, which contained a scene specially written to allow him to perform his party trick of wiggling his toes. More than just an actor, he became a regular on the radio show, Just a Minute. His death, from pneumonia, occurred a few weeks after a domestic fall which left him in a coma at the Chelsea and Westminster Hospital, London.