Campbell studied at the London drama school Royal Academy of Dramatic Art in the early 1970s, he founded a theater group that occurred in unusual places such as pubs. Among the members of his group included, among others, Bob Hoskins.
In 1976 he was co-founder of the Science Fiction Theatre of Liverpool, which it had set itself the goal Illuminatus! to bring to the stage after the trilogy by Robert Anton Wilson and Robert Shea. He also appeared as a performer himself on to the other actors also included Bill Nighy. The play was performed at the Royal National Theatre. Another major project of the Science Fiction Theatre of Liverpool was the stage adaptation of The Hitchhiker's Guide to the Galaxy on the novel by Douglas Adams in which he played the role of Arthur Dent. However, this was not very successful, but Adams then wrote a role for him in radio production at the BBC.
Campbell had in the 1970s, guest-starring roles in various British television series such as Fawlty Towers and The Professionals. In the 1980s, he starred in several major theater productions such as Pauline and Joshua, Bride of Frankenstein and A Fish Called Wanda. In addition, Campbell worked as a writer, and has published numerous books.