He joined The Tyme in 1965 who played at local youth clubs. Thompson's next group was a local band called The Urge which he joined when 17 years old. Fatigue from performing with them seven nights a week in local clubs and pubs led him to fall asleep on his job as an apprentice metalworker, which resulted in his dismissal.
He was a member of The Influence with John Miles. Thompson joined Roxy Music in 1971 and was credited as drummer on six albums, as well as touring and performing on solo records with his bandmates Bryan Ferry, Brian Eno, Andy Mackay and Phil Manzanera. In 1980, Thompson took leave from Roxy Music due to a thumb injury. Later that year he left the band due to musical differences between himself and Bryan Ferry. During this period Thompson played with rock band Concrete Blonde.