Quinn's stay at Leicester lasted less than nine months, and he scored a mere six goals from 31 appearances, most of which were as a substitute. In March 1989, he moved to Bradford City for £210,000, where he scored 14 goals in 35 games before moving again in December 1989, this time to West Ham United, who had recently been relegated from the First Division. The fee was £320,000, the highest sum paid for Quinn during his career. During his time at the club, Quinn scored eighteen league goals in forty-seven games, playing a part in their return to the First Division. It was here that Quinn earned his nickname of "Jimmy the Tree", as he did not seem very mobile on the pitch although he did score a good return of goals helping West Ham return to the First Division in 1991. However, Quinn did not play in the top flight, instead transferring to Bournemouth of the Third Division at the start of the 1991–92 season. Although he only spent a single season at the south coast club, he scored nineteen goals in forty-three games.