Cockram joined Tottenham Hotspur as an apprentice in January, 1981. The winger went on to make two appearances for the Lilywhites. He transferred to Bristol Rovers in August, 1985 and played in one first team match. Cockram joined St Albans City where he was voted Player of the Season 1987-88 and would later become their manager in 1995-96. In March, 1988 he joined Brentford and he featured in 90 matches and scored 14 goals. After leaving Griffin Park he played for Woking before ending his senior career at Reading where he notched up a further six appearances and netting a solitary goal.