Wells started in cabaret at Oxford and began his television career as a writer on That Was The Week That Was, the 1960s weekly satire show that launched the careers of David Frost and Millicent Martin, among others, and also appeared in the television programme Not So Much a Programme, More a Way of Life, as well as in The Secret Policeman's Other Ball. Besides making cameo appearances in films such as Casino Royale (1967) and Rentadick (1972), television dramas like Casanova (1987), an episode of Lovejoy (1991) and comedy shows like Yes Minister, he also wrote television scripts and screenplays, such as Princess Caraboo (1994).

In 1971, with John Fortune, he published the comedy classic A Melon for Ecstasy, about a man who consummates his love affair with a tree. Wells played the headmaster of Thursgood's Preparatory School in Tinker, Tailor, Soldier, Spy (1979).