Potts was West Ham United Club captain for a 3 years between 1993 and 1996, and was voted Hammer of The Year in 1993 and 1995, and runner up in both 1992 and 1994. During his career he amassed a total of 505 appearances for the club (good enough for ninth place in the club's all-time appearance charts), scoring only one goal, in a 7–1 win against Hull City in 1990. His last competitive appearance for the club was on 7 March 2001 against Chelsea, although he stayed on until 2002. In 1997 he was awarded a testimonial by West Ham. The game was played on 2 August 1997 and was a 2–0 win against QPR.