Before Rockpile, he played with The Luvvers, who served as Lulu's backing band and recorded a single ("The House On The Hill"/"Most Unlovely") for Parlophone in 1966. In 1971 he added some guitar work to March Hare, the first solo album from ex-Honeybus member Colin Hare.
Immediately before Rockpile he was a member of the Neil Innes band Fatso, which went on to record the soundtrack for the original Rutland Weekend TV program.
After Rockpile split in 1981, Bremner played lead guitar on The Pretenders' 1982 single "Back On The Chain Gang/My City Was Gone". He 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 Burch, Elvis Costello, and Chris Difford and Glenn Tilbrook of Squeeze.
After stints in Los Angeles, California (where he played in the bands of Pat McLaughlin and Rosie Flores) and Nashville, Tennessee he moved to Sweden in the 1990s where he hooked up with The Refreshments, producing and playing on a few of their albums. 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.