A winger, Cockram joined Tottenham Hotspur as a schoolboy in 1975 and went on to make two first team appearances for the Lilywhites towards the end of the 1983–84 season.
[5] A move to Isthmian League Premier Division club St Albans City during the latter part of the 1986–87 season, in a bid to return to fitness following an achilles injury,[6] proved to be the turning point in Cockram's career.
[7] After a successful period training full-time with Brentford during the 1987–88 season,[6] Cockram signed a contract with the club in March 1988.
[9] Cockram finished his career with spells at non-League clubs Chertsey Town and Leatherhead.
[13] Fellow former footballer David Beckham, and his son Romeo, met the Mighty Penguins team in September 2023, and presented Cockram with The Sun's Who Cares Wins Unsung Hero Award.