Born in Accrington, Lancashire,[2] Duxbury began his career as a right back with Everton, but he signed for Manchester United as a schoolboy in 1975.
Duxbury made his Manchester United debut on 23 August 1980, coming on as a substitute for Kevin Moran against Birmingham City.
Duxbury became a semi-regular in the first team over the next couple of seasons, although – due to the form of first-choice full backs John Gidman and Arthur Albiston – he spent most of his time playing at centre-back; it was not until towards the end of the 1981–82 season that Duxbury began to play in his favoured right back position.
The following season, he won his first FA Cup medal with Manchester United, playing in both matches of the 1983 final against Brighton & Hove Albion.
He continued at Manchester United for another five years, but he found his first-team opportunities increasingly limited as he began to play more reserve matches.