Webb joined Reading on leaving Little Heath School in 1979 and made his first-team debut in February 1980 at the age of 16. He became the youngest ever scorer for the Berkshire side.
In July 1982 he transferred to Portsmouth for £87,500. At Fratton Park he was a regular first-team player and helped them win promotion to the Second Division (as Third Division champions) in his first season, and over the next two seasons they came close to reaching the First Division.
In 1985, Nottingham Forest manager Brian Clough paid Portsmouth £250,000 for Webb. At Forest he developed into a top class midfielder with a strong goalscoring record. During his time on Trentside he won the League Cup in 1989 (scoring in the final against Luton) and became a regular member of the England national team from 1987. Webb was one of the Forest players who had to cope with the horrors of the Hillsborough disaster during the opening minutes of their FA Cup semi-final against Liverpool. Webb played in the rescheduled game at Old Trafford, which Liverpool won 3–1. He scored Forest's only goal of that game.
His goalscoring record at Forest exceeded that of many strikers at the time. He managed 14 league goals in both of his first two seasons at the club, in 1986–87 from just 32 games. This included a hat-trick against Chelsea in September 1986 that sent him to the top of the League's scoring charts. He scored 13 times in the 1987–88 league campaign, though his goalscoring totally was lower in 1988–89 (six goals from 30 games) it did nothing to diminish his reputation as a first class midfielder. He scored for Forest against Luton Town in the 1989 Football League Cup Final which they went on to win.
Robson also gave Webb his full international début, against West Germany on 9 September 1987 at the age of 24. His first goal came against Turkey on 14 October that year, in an 8–0 victory at Wembley in a Euro 88 qualifier. He appeared in two of England's group games at Euro 88 (which all ended in defeat), but his next international appearance – against Denmark in a friendly on 14 September 1988 – he scored the only goal in the game at Wembley. On 3 June 1989, he scored the third international goal of his career with a 3–0 World Cup qualifier victory over Poland, again at Wembley. On 24 April 1990 Webb made his first appearance with the England B team, playing in the 2–0 win over the Czechoslovakia B team at Roker Park. Despite missing the bulk of the 1989–90 season at Manchester United with injury, he was included in England's 1990 World Cup squad and made his solitary appearance of the competition in the third place playoff defeat by Italy. Before the year was out he would become the first player to be sent off whilst on England duty in three years when he saw red for the England B team in a match against the full Algeria team. On 12 May 1992, he scored what would be his final goal for England in a 1–0 friendly win over Hungary in Budapest. He would make four more international appearances for England, the last cap of his 26-cap, four-goal international career coming on 17 June 1992, on the fateful night that England lost 2–1 to hosts Sweden in their final Euro 92 group game, and squandered hopes of reaching the last four of the eight-club competition. Webb was capped 26 times in five years for the England team, and was also the 1,000th player to be capped by England.
In July 1989 he joined Manchester United. The transfer fee of £1.5 million was determined by a transfer tribunial (Forest manager Brian Clough, reluctant for Webb to leave, offered to pay this to keep him). Webb scored on his league debut on 19 August 1989, when they achieved a 4–1 home win over defending league champions Arsenal on the opening day of the 1989–90 season.
In the 1990 FA Cup final, he memorably hit a clinical 50-yard pass to Lee Martin who subsequently scored the winning goal in the FA Cup Final replay.
He played in 31 out of 42 First Division games for Manchester United in 1991–92, but missed the final few games of the season due to a rift with manager Alex Ferguson – some fans even blamed United's failure to win the league title that season on Webb's absence from the final games. He was also faced with stiff competition for a place in the centre or on the right of midfield - as well as Bryan Robson and three midfielders who had joined United in 1989, he was now faced with competition from Soviet winger Andrei Kanchelskis.
He returned to Nottingham Forest for £800,000 on 23 November 1992. His second spell at Forest was unsuccessful, as he could not win a regular first-team place because of the emergence of other players like Steve Stone and Lars Bohinen. He made just nine league appearances in 1992–93 as Forest were relegated, but when manager Brian Clough retired and was succeeded by Frank Clark, he had more first team opportunities, playing 21 league games and scoring three goals as Forest were promoted back to the Premier League as Division One runners-up.
Webb never played league football for Forest again after the 1994 promotion, though he remained contracted to the club for another two years.
He had a spell on loan back at Reading in the 1995–96 season before finally leaving Forest for good in the summer of 1996.
After having to give up playing football, from June to December 1997 he was player-coach of Southern League Southern Division side Weymouth, but quit after just 70 days. His next spell in management with non-league Reading Town in 2001 was also short-lived.
In a 2005 vote to compile the Royals' best-ever eleven, Webb was voted on the team in central midfield.
He joined United at a time when they were entering their fourth season under the management of Alex Ferguson, but had yet to win a major trophy under him in spite of heavy spending on new players – with Webb arriving around the same time as Danny Wallace, Mike Phelan and Gary Pallister.
