Compton was born at London. He began publishing with his 1962 novel Too Many Murderers. His 1968 novel The Steel Crocodile (alternate title The Electric Crocodile) was nominated for the Nebula Award, and his 1974 novel The Continuous Katherine Mortenhoe was filmed as Death Watch by Bertrand Tavernier during 1980. His 1968 novel Synthajoy was very similar in content to the 1983 film Brainstorm.
He was named the 2007 Author Emeritus by the Science Fiction and Fantasy Writers of America.