Nimmo was born in Liverpool, Lancashire, the son of an insurance salesman, and grew up in Mossley Hill in an environment he described as "old merchant's houses, comfy English suburbia". He was educated at Booker Avenue Infants and Junior School as well as Quarry Bank High School for Boys, then a grammar school under headmaster R. F. Bailey, who brought with him, from his previous position as assistant headmaster at leading independent school Shrewsbury School, "the finest traditions of public schools". He then followed his father into the insurance business, and after National Service in Cyprus, became a salesman for a paint company. He began his stage career at the Hippodrome Theatre in Bolton, Lancashire. It was during this time that he made a cameo appearance in the Beatles' film, "A Hard Day's Night" (in which he appeared as "Leslie Jackson", a magician with doves).