Bremner first came into the limelight in 1985, when his single, N-N-Nineteen Not Out (released under the name, "The Commentators") was a big hit in the British charts. It was a parody of Paul Hardcastle's number one hit, 19, with Bremner impersonating cricket commentators, including Richie Benaud and Brian Johnston, and replacing references to the Vietnam War with references to the 1932-3 "Bodyline" cricket tour. The record was produced by Hardcastle under a pseudonym.

Bremner soon had his own BBC2 show, and later moved to Channel 4, where his output became more satirical and the sporting commentators gradually came to represent a smaller proportion of his repertoire. Having teamed up with veterans, John Bird and John Fortune, he now hosts Bremner, Bird and Fortune, which (along with its predecessor Rory Bremner, Who Else?) has won numerous awards. Occasional one-off specials are also shown, with Bremner impersonating Tony Blair and various other government figures. In the 1990s he became a semi-regular cameo turn on the Channel 4 improvisation show Whose Line Is It Anyway? and in 2005 he was a team captain on the BBC2 improvisational satire show Mock The Week.

Educated at Clifton Hall School and Wellington College, Bremner then studied at King's College London and he was awarded Honorary Life Membership of King's College London Students' Union in the early 2000s. In 2005 he accepted an Honorary Fellowship at King's.