Brandon's music career started in 1978, in Clapham, South London, with the formation of punk group The Pack, in which he was the singer/songwriter. The Pack consisted of Brandon, Scottish-born drummer Rab Fae Beith and two Canadian brothers, Simon and Jon Werner on guitars. The last live gig by The Pack took place at a sold out 101 club in Clapham.
Brandon then formed the post punk new wave band Theatre of Hate in 1980 recruiting Stan Stammers on bass guitar, Nigel Preston on drums, Billy Duffy on guitar and John 'Boy' Lennard on saxophone. Theatre of Hate had their largest hit from the Westworld album with the single "Do You Believe In The West world?", which achieved #40 in the UK Singles Chart in January 1982, while the album rose to #17 in the UK Albums Chart in March 1982.
Theatre of Hate disbanded in 1983. Brandon and Stammers were then joined by Lascelles James on saxophone and Chris Bell on drums to form Spear of Destiny. The new band adopted a more melodic and less aggressive sound, distancing them from post-punk and moving a little more towards mainstream pop.
While continuing to explore the political ideas that he wrote about in Theatre of Hate, Brandon's lyrics for Spear of Destiny dealt more frequently with the classic pop themes of love and romance. Many line-up changes followed with the band swelling to a 6 piece and then contracting back to a 4 piece. The band's reputation as a live act never translated itself into record sales, and Spear of Destiny only scored one Top 20 hit.
In 2003, Brandon did a solo tour as support to The Alarm on their 'Poppyfields' tour. His set included some new material played on an acoustic guitar with electric pick up, as well as some material from his time with Theatre of Hate and Spear of Destiny. In later years he performed in the punk supergroup, Dead Men Walking, before reforming and touring with Spear Of Destiny in 2007 and 2008.