He was a school friend of Robert Smith, Michael Dempsey, and Lol Tolhurst and played with them in various local bands, eventually evolving into the Easy Cure.

[5] During this period, Thompson performed music part-time, as a member of The Exotic Pandas and as an occasional contributor for The Glove (a side project by Robert Smith and Steve Severin).

While observing the Cure in the studio in late 1983, Thompson was invited by Smith to play saxophone on a song that would be included in The Top the following year.

[7] When Robert Smith revamped the Cure's lineup in 1984, Thompson became the band's lead guitarist and occasionally played keyboards and other instruments.

In the late 1990s he made guest appearances on albums by Presence and Babacar, both founded by other former members of the Cure, and formed his own short-lived band called Quietly Torn.

[13] Thompson and Andy Vella began an artistic partnership in the early 1980s and later co-founded the design firm Parched Art.

[16] In 2015, Thompson held his first exhibition in the United States, with abstract landscape paintings displayed at MusicHead Art Gallery in Los Angeles under the title "...Through the Eyes of Birds".

[2] He then pursued an advanced art degree at the University of Brighton; while a student in 2020, he created the pictorial book Ways of Dying, illustrating types of deaths recorded in London in 1632.