During his playing career, Buxton played in the Football League for both Burnley and Halifax Town, making a total of 53 professional appearances in nine seasons. He was plagued with injuries and broke his tibia twice while playing for Burnley.
Buxton initially joined Huddersfield Town in late 1977 from Southend United as Trainer (Physiotherapist). After Tom Johnston's resignation in 1978 Buxton was appointed manager of Huddersfield Town. He would eventually go on to be one of the most successful managers in the club's recent history, winning promotion to the Third Division in 1980 and the Second Division in 1983. The Terriers would remain in the second tier for five seasons, but Buxton was sacked on 23 December 1986, to be replaced by Steve Smith. Buxton returned to Town in March 1993 as coach under Ian Ross but resigned after Ross resigned.
Scunthorpe United would be Buxton's next managerial appointment. He remained there for four years, with the team occasionally mounting a promotion challenge in this period. He left by mutual consent on 31 January 1991. He returned to Scunthorpe in 1996, but left the following year.
Following the dismissal of Terry Butcher with the side in the relegation zone, Buxton would be appointed Sunderland manager in 1993. A tightening of the team's defence led to an improvement in results and Sunderland finished the 1993-94 season in 12th place. Although a reasonable defensive record was maintained the following season, Sunderland were entangled in a relegation struggle and Buxton would be replaced by Peter Reid.