Cooke began his career in the youth system at Mansfield Town and made 9 appearances and scoring one goal in his debut season, in which the Stags won the 1976–77Third Division championship. He made only six appearances in Second Division during the 1977–78 season and departed the club at the end of the campaign, having made just 15 first team appearances for the club.
Cooke joined Southern League First Division North club Grantham during the 1978 off-season and scored 43 goals to propel the club to the 1978–79 division championship. Cooke's performances saw him awarded the Supporters' Player of the Year award. Grantham moved to the Northern Premier League for the 1979–80 season and Cooke was on fire again, scoring 39 goals. He departed the Gingerbreads at the end of the campaign.
Peterborough United
Cooke's goalscoring exploits for Grantham caught the eye of Fourth Division club Peterborough United, which culminated in him moving to the club for a £12,000 fee in May 1980. He was an immediate hit at Posh, scoring 29 goals in 56 games during the 1980–81 season and being named in the Fourth Division PFA Team of the Year. Cooke bettered his goalscoring tally in the 1981–82 season, with 31 goals in 55 games. Cooke's prolific form tailed off during the 1982–83 season and he managed only 11 goals in 33 appearances before departing in February 1983. Cooke scored 71 goals in 144 appearances for the Posh.
Cooke signed for Second Division club Cambridge United in February 1983 for a £12,000 fee. He failed to find his prolific goalscoring form for the struggling club, which suffered relegation to the Third Division at the end of the 1983–84 season. Cooke managed 14 goals in 65 league appearances and with relegation to the Fourth Division looming, he departed the club midway through the 1984–85 season.
Brentford (loan and permanent transfer)
Cooke joined Third Division club Brentford on a two-month loan in December 1984 and he later signed permanently for a £20,000 fee He quickly found form, scoring 16 goals in 31 games and scoring what proved to be a consolation in the 3–1 1985 Football League Trophy Final defeat to Wigan Athletic. Cooke finished the 1984–85 season as both Brentford and Cambridge United's top scorer, which was only the third time in history the feat had been managed. Three years of mid-table mediocrity followed and Cooke departed Brentford in December 1987, having scored 64 goals in 150 games for the Bees.
Cooke joined Second Division high-flyers Millwall on 11 December 1987 for a £30,000 fee and scored one goal in five appearances during the remainder of the 1987–88 season. He was unable to break up the forward pairing of Tony Cascarino and Teddy Sheringham and departed the Lions in September 1988.
Cooke dropped back into Non-League football to join Conference club Kettering Town in September 1988. He had a prolific spell with the Poppies, scoring 49 goals in 95 appearances across three seasons in which the club consistently challenged for promotion to the Football League.
