Best known for his work as guitar player of Rockpile which played on the bulk of Nick Lowe's and Dave Edmunds' albums throughout the mid 1970s. Bremner acted as lead vocalist on the odd Rockpile song, including on the only album credited to Rockpile, Seconds Of Pleasure, released in 1980. He also wrote Edmunds' hit Trouble Boys, but used an alias so as not to be confused with the more famous footballer.

He played with The Luvvers, who were Lulu's backing band in the early 1960s.

After Rockpile split in 1981, Bremmer played lead guitar on the Pretenders' 1982 single Back On The Chain Gang/My City Was Gone.

Bremner released his first solo album BASH! in 1984, including songs co-written with Elvis Costello and Chris Difford and Glenn Tillbrook (of Squeeze). A second album, A Good Week's Work, followed in 1999. After stints in LA and Nashville, he moved to Sweden in the 1990s where he recorded a few albums with The Refreshments. In 2006, Bremner released his third solo album, No Ifs, Buts, Maybes.