He began his playing career with local club Darlington, making his debut for them back in the 1982-1983 season. Thereafter he became the Quakers first choice goalkeeper for three seasons before moving to Everton as cover for the Welsh goalkeeper Neville Southall in April 1986.
Spending just six months at Goodison Park with the then English champions, he moved to Walsall for a fee of £100,000. He replaced Mark Prudhoe in the Saddlers goal for the win against Rotherham United in October 1986, and kept his place in the first team for the majority of that campaign. Despite eccentricites such as donning a mask when entering the field of player, Barber was a hugely popular figure amongst Walsall fans, and he played a crucial role in the club's Division Three play-off final replay victory in the 1987-88 season over Bristol City. Indeed, after the two-legged final had ended in a 3-3 aggregate draw, Barber saved two penalties in the subsequent penalty shootout which determined who would have home advantage in the replay. Walsall took advantage of this home advantage, and Barber kept a clean sheet as Walsall romped home to a 4-0 victory.
The purchase of Ron Green in 1989 saw Barber lose his foothold as the number one custodian at Walsall and he spent time out on loan with Peterborough United, Chester City (twice) and Blackpool over the next two years.
Indeed it was Peterborough who snapped him up on a permanent basis in the summer of 1991.
After temporary spells with Chesterfield and Colchester United it was Luton Town that signed him in the summer of 1994. However, he did not make an appearance for the Hatters due to the emergence of young goalkeeper Kelvin Davis so was on the move again.
Peterborough took him back to their club for a five-game loan spell to cover for injuries, with Ipswich Town (November 1995) and Blackpool (December 1995) doing likewise.
Birmingham City eventually secured his permanent registration in January 1996, but he was to play just two games for the Blues when covering for old Peterborough team-mate Bennett and the Dutchman Bart Griemink, before an injury forced his premature retirement from the full-time game.
In the summer of 1996 he was appointed as a part-time goalkeeper coach with Bolton, in a role which was to be made permanent a few years later. Initially, he also combined his role at the Wanderers with part time spells at West Bromwich Albion and Burnley as well as one final fling as a player with Kidderminster Harriers in 1997.
Nearly six years after his retirement he contemplated a playing comeback with Bolton as they had been short on goalkeeping cover mid-way through the 2001-2002 season. Steve Banks had been ruled out with a broken finger, thus leaving Finnish international Jussi Jääskeläinen as the club's only recognised goalkeeper.
Barber offered to sign a playing registration which enabled him to sit on the substitutes bench in case of an emergency, but his request was politely turned down by the Bolton manager Sam Allardyce who was willing to take the risk until Banks resumed his fitness.
This was a decision which came back to haunt Allardyce, as Jaaskelainen was sent off in the next game against Newcastle United, meaning that the Trotters midfielder Bo Hansen was required to go in the goal for most of the match.
In the winter of 2004, Barber ended his remaining commitments with West Bromwich Albion as their manager Bryan Robson appointed his former England team-mate Joe Corrigan as Albion's full time goalkeeper coach.
Robson felt that Barber's lengthy involvement with Bolton would hinder the coaching of Albion's goalkeepers, this giving Barber the chance to spend more time with the members of the Wanderers squad.
Outside of day to day training, Barber and fellow goalkeeper coach Malcolm Webster run a goalkeeping school for young and budding footballers. He also continues his freelance work for other clubs when his Bolton commitments allow, with Rochdale F.C. just one of the clubs to benefit from his expertise as a leading coach in his field.
Barber and Glynn Snodin were announced as the coaching staff to support Nigel Worthington upon his appointment as the manager of Northern Ireland on 2007-06-01.
In November 2007 speculation was rife that Barber would rejoin his friend Sam Allardyce as goalkeeping coach at Newcastle United following the departure of Terry Gennoe due to injury but Barber remained loyal to Bolton and signed a new contract. Instead the position was filled by Paul Barron.