He was born in Liverpool, England, a city with which he is firmly associated in most people's minds. He was educated at the University of Hull, and in the early 1960s he met Mike McGear, along with John Gorman, another multi-talented entertainer. Together, they formed The Scaffold, a comedy group, hitting number one in the British charts in 1968 with Lily the Pink. McGough co-wrote many of their songs and is the only one of the three whose fame survived the group's demise. He continues to perform widely.
McGough was also responsible for much of the humorous dialogue in The Beatles' animated movie Yellow Submarine, although he did not receive an on-screen credit for it.