Graham founded Atomic Rooster with Vincent Crane and Carl Palmer in 1969, and appeared on the band's first album.

In 1977, Graham formed Alibi, as a songwriting project with drummer Tony Knight, who was later replaced by Charlie Morgan.

In 1985, Graham performed as part of the Explorers with former Roxy Music members Phil Manzanera and Andy Mackay.

He subsequently began songwriting for other artists, including the Cheap Trick hit single "The Flame", which he co-wrote with Bob Mitchell in 1988, as well as "Remember My Name" for House of Lords, which reached No.

He has since performed with David Jackson, Jess Roden, the Reduced Shakespeare Company and the Jim Capaldi Band.