Burrows completed an apprenticeship at West Bromwich Albion and signed professional forms with the club as a 17-year-old in 1985, after a period in the Tipton Town youth team.
He along with the rest of Liverpool Football Club were commended for the way they conducted themselves after the disaster and he attended numerous funerals and comforted the victims' families and friends.
At this time he was not regularly featuring in the team, with the equally inexperienced Steve Staunton enjoying an extended run at left back which lasted through to the end of the season, including the 3–2 FA Cup final victory over Everton in which Barry Venison was selected for a place on the substitute's bench ahead of Burrows.
The following year, with Staunton more frequently deployed in midfield and manager Dalglish prepared to rotate his squad more, Burrows played more regularly and won his first honour with Liverpool when they clinched the League title, finishing nine points clear of Aston Villa.
[1] When Dalglish quit in 1991 and was replaced by Graeme Souness, Burrows found his chances more restricted, though he did score his first Liverpool goal on 31 August 1991 in a 3–1 victory over Everton at Anfield.
[2] 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[2] 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.
[1] In March 2002, Sheffield Wednesday signed Burrows on a free transfer and yet again he made a quick début, this time the following day, in a 0–0 league draw against Gillingham at Hillsborough.