Bremner first became known playing with The Luvvers, who served as Lulu's backing band. However, by the time Bremner joined the group in 1966, they were on the wane; Bremner did not play on any of Lulu's recorded material, and joined just after the group recorded their only single without Lulu for Parlophone in 1966. The Luvvers disbanded in 1967. In 1971 Bremner added some guitar work to March Hare, the first solo album from ex-Honeybus member Colin Hare. He then became a member of the Neil Innes band Fatso, which went on to record the soundtrack for the original Rutland Weekend Television series. As "Bill Murray" he released two singles produced by Kris Ife; "Downtown hoedown"/"Rhyme and reason": Polydor 2058 881, and "Heart and the Stone"/"I Don't Wanna Be No Hero" State records 72. Next, he joined Rockpile, who only released one album under their own name, but also served as the band for most of Nick Lowe's and Dave Edmunds' albums in the 1970s. In addition to his guitar playing, Bremner occasionally sang lead, as he did on "Heart" and "You Ain't Nothing But Fine" on the 1980 Rockpile album Seconds of Pleasure. He also wrote Edmunds' hit "Trouble Boys", but used an alias, Billy Murray, on the writing credits, so as not to be confused with the more famous Scottish footballer, of the same name. "Trouble Boys" was covered by Thin Lizzy on a single in 1981. Another song by him, The Creature From the Black Lagoon, appeared on Edmunds' third solo album, Repeat When Necessary. After Rockpile split in 1981, Bremner released two solo singles on Stiff Records "Loud Music In Cars"/"The Price is Right" and "Laughter Turns to Tears"/"Tired and Emotional". Bremner then played lead guitar on The Pretenders' 1982 hit single "Back On The Chain Gang"/"My City Was Gone" and later provided lead guitar for their 1990 album Packed!. Bremner released his first solo album, Bash!, in 1984, containing songs co-written with The Records' Will Birch, and covers of songs by Elvis Costello, and Chris Difford and Glenn Tilbrook of Squeeze. Bash! featured a rhythm section of Dave Kerr-Clemenson from Fast Buck on bass and Terry Williams from Rockpile on drums. Bremner played all the guitar parts and sang the harmonies with Kerr-Clemenson. Billy could be seen many times at the legendary Red Lion Brentford playing with Fast Buck. After stints in Los Angeles, California and Nashville, Tennessee Bremner moved to Sweden in the 1990s where he met The Refreshments, producing and playing on their album It's Gotta Be Both Rock 'n' Roll. A second solo album, A Good Week's Work, followed in 1999 and a third No Ifs, Buts, Maybes in 2006, both recorded in Sweden. His most recent solo album, Rock Files, was issued in 2012. Bremner, Sean Tyla and two Swedish musicians, are also members of Stockholm-based band Trouble Boys, who released an album Bad Troublein September 2012