Burrows left for West Ham United in September 1993, along with Mike Marsh, as part of a deal that took Julian Dicks to Anfield. He had appeared 193 times for the Reds, scoring three goals. Burrows made his West Ham debut in September 1993, just a day after joining them, in a 2–0 league win over Blackburn Rovers at Ewood Park. He spent just a single year at Upton Park, appearing 35 times scoring twice; in his second West Ham game in a 5–1 League Cup win against Chesterfield and in a 3–1 home win against Manchester City Although he started the 1994-95 season, he played only four games before moving to Everton as part of a deal which saw the return of Tony Cottee to West Ham.
Burrows joined Everton in September 1994, but his time at Goodison Park was short lived. He spent just six months at Everton, playing 23 times, before he was on the move again, this time to Coventry City, in March 1995. Burrows featured in the early stages of Everton’s glorious 1994–95 FA Cup campaign before leaving, starting the third and fourth round ties against Derby County and Bristol City respectively.