As a player, he was a goalkeeper, who notably played top-flight football for Wimbledon, Newcastle United, Chelsea, Southampton and Nottingham Forest.

Since retiring, Beasant has worked as a goalkeeping coach for Fulham, Northern Ireland, the Glenn Hoddle Academy, Bristol Rovers, Stevenage and Reading.

Beasant entered the Football League in 1979 at the age of 20 when Wimbledon, newly promoted to the Third Division, signed him from his local non-league club Edgware Town.

He became the first goalkeeper to save a penalty in an FA Cup final when he blocked John Aldridge's spot-kick for Liverpool in 1988, and in doing so helped Wimbledon secure a 1–0 win.

Between 1981 and 1990 (across most of his time with Wimbledon, the season at Newcastle and the start of his Chelsea spell) he made 394 consecutive league appearances, the second-highest sequence in English football history.

[8] During the 1993–94 season Beasant sustained an unusual injury when, while making a sandwich in his kitchen, he dropped a 2 kg glass bottle of salad cream on his foot,[9][10] severing the tendon to his big toe.

[12] Following the arrival of new manager, Glenn Hoddle, who opted for Dmitri Kharine as his first choice keeper with Kevin Hitchcock in reserve, Beasant was unable to get back into the Chelsea squad and looked for a new club.

Following the arrival of Paul Jones in the summer of 1997, Beasant was now only third-choice 'keeper, and after a loan move to Nottingham Forest in August 1997, the transfer was made permanent in November.

[citation needed] He came out of retirement on 17 August 2013 to play for Southern League Division One Central club North Greenford United in a 2–0 defeat against Chalfont St Peter.

[19] Having joined Stevenage as the club's goalkeeping coach in the middle of 2014, Beasant was named as a substitute for an away match at Carlisle United on 11 October 2014, aged 55.

The first of Beasant's two England caps came at Wembley Stadium on 15 November 1989 against Italy in a friendly match, where he replaced Peter Shilton as a half-time substitute and kept a clean sheet in a 0–0 draw.