He played on the 10cc Live: King Biscuit Flower Hour album recorded in 1975 and officially joined 10cc as drummer, percussionist and occasional keyboardist in 1976 after the departure of Kevin Godley and Lol Creme.

Burgess subsequently became a member of The Invisible Girls, a band that backed punk-influenced performance poet John Cooper Clarke on several of his late 70s/early 80s recordings.

The following year 1982, Burgess was briefly a member of Jethro Tull, replacing Gerry Conway, and touring throughout Europe and North America with the band.

He was the drummer on the London Symphony Orchestra's album A Classic Case, which also included the rest of the current Jethro Tull members.

During the late 1980s, Burgess also did extensive live work with a range of artists including glam-rocker/rockabilly revivalist Alvin Stardust and disco singer Gloria Gaynor.

In 1990, Burgess replaced drummer Zak Starkey in a late-running version of the new-wave rock band The Icicle Works.

[8] In 2022, Burgess joined singer-songwriter Clive Gregson, Neil Cossar (The Cheaters) and bassist-singer Craig Fletcher and Keyboardist Jez Smith from Barclay James Harvest to form The Guilty Men.