[5] Adcock became a prolific scorer for Colchester, and established himself in the first-team squad following the death of John Lyons and the departure of Kevin Bremner.
[3][10] In January 1988, Adcock was signed by Northampton Town in exchange for Trevor Morley[8] and the £85,000 fee was a record figure for the club at the time.
[11] During his first spell at Northampton, he netted 30 goals in 72 league appearances, but when the Cobblers were relegated to the Fourth Division in the 1988–89 season, he secured a £190,000 move to Bradford City in October 1989.
[3] The club's financial plight proved to be a blessing for Adcock as he scored 10 goals in 35 appearances, eventually being offloaded to Peterborough United in a £35,000 deal.
[13] He scored 35 league goals in total for Peterborough in 111 appearances from 1992 to 1994, aiding the club to promotion to the newly restructured Division One via the play-offs in 1992.