Mullery was a key player for the Spurs teams that won the FA Cup in 1967, and skippering them to victory in the 1971 Football League Cup Final and the 1972 UEFA Cup Final. In the '72 UEFA Cup Final, his header in the 2nd leg was the decisive goal in a 3–2 aggregate victory over Wolverhampton Wanderers. Mullery was also in the Fulham team that lost the 1975 FA Cup Final to West Ham United.