Kevin Bremner, born in Banff, began his senior career as an 18-year-old with home-town club Deveronvale of the Highland League; he had been with the club since he was 14 years of age. In the 1977-78 season, he was part of the team which defeated Huntly to win the Bell’s Cup; he finished the season as leading scorer with 27 goals and won the club’s player of the year award.
Celtic manager Billy McNeill has invited him for a two-week trial, but no contract offer ensued and Kevin left Deveronvale for fellow Highland League club Keith.
In October 1980 he moved to England to join Colchester United of the Third Division for a fee of £40,000; that season Colchester were relegated to the Fourth Division. Kevin played more than 100 matches for Colchester in all competitions, and during the 1982-83 season he spent short periods on loan at Birmingham City, Wrexham and Plymouth Argyle scoring goal for each.
In February 1983 he joined Millwall for £25,000. His first goal for the club gave him the distinction of having played and scored in the Football League for five different clubs in the same season. Kevin played more than 100 games in all competitions for Millwall, helping them gain promotion to the Second Division as Third Division runners-up.
At the beginning of the 1984–85 season he joined Reading; as the clubs were unable to agree on a transfer fee, the Football League tribunal valued his services at £35,000. In his second season at the club, he contributed to Reading winning the Third Division title, before joining Brighton & Hove Albion in 1987, where for the third time in four seasons he played his part in his club gaining promotion from the Third Division. He finished the season as the club’s leading scorer, with 12 goals in all competitions. Between 1987 and 1990 Kevin played 141 matches for the Seagulls scoring 40 goals.
He spent a season at Peterborough United before returning to Scotland where he signed for Dundee contributing to their First Division title in 1991-92.