Bennett was born in Manchester and began his playing career with Manchester City, joining the club's youth side along with his brother Gary. He made his first senior appearance for them in the 1978–79 season during a 0–0 draw with Everton on 14 April 1979 as a substitute in place of Tommy Booth, and becoming a first team regular the following season. The following year, Bennett was used mostly as a backup but his performances in the team's progression to the semi-finals of the Football League Cup, scoring five times in the previous four matches, saw him selected for the 1981 FA Cup Final against Tottenham Hotspur.