After picking up the saxophone when he was 15, Hamilton spent the early 1970's playing for Smiling Hard[2] at the Top Ten Club on the Reeperbahn. They went on to tour Europe and Australia and were often hired by US artists, notably playing for Edwin Starr[3] and Ben E. King. In 1979, Hamilton recorded "H.A.P.P.Y. Radio"[3] and toured America with Starr.
Upon moving back to London, Hamilton met Tony Visconti, later playing on several Visconti productions. Through this, Hamilton met Colin Thurston and went on to record the 'night' version of "Planet Earth". Hamilton toured alongside Duran Duran during the 1980's and played a saxophone solo on "Rio". He did three world tours alongside the Durans—Sing Blue Silver during 1983–84 and the Strange Behaviour Tour in 1987, in support of the Notorious album, where he met and performed alongside Lou Reed. He later toured worldwide with the reunited Durans during their 2003 reunion tour.
In 1982, Hamilton joined Dexy's Midnight Runners, whom he toured extensively with in the US and Europe during their rise to fame after their single "Come On Eileen".[4] After being pulled off stage one night in France, Hamilton met David Bowie, who let him feature in some music videos, notably "Wild Is the Wind" and "The Drowned Girl".[5]
Hamilton has composed theme and incidental music for television and film in both the US and the UK. He has a songwriting partnership with guitarist Phil Palmer, and they won the UK Songwriting Contest in 2015 with the song "Everything's Great All The Time".[11] As well as saxophones, Hamilton also plays keyboards and EWI (electronic wind instrument).