Born in Wolverhampton, Cocker began his career in the youth team of Wolverhampton Wanderers in 1956, playing in their 1958 FA Youth Cup triumph. He turned professional in Summer 1958 and eventually made his senior debut on 4 February 1961 in a 2–1 defeat at Blackburn Rovers. This turned out to be his only appearance for Wolves' first team and he was released at the end of the season.
He joined local non-league side Wellington Town immediately after, playing in over 200 games during the 1960-61 season. After breaking a collar bone, he left and relocated to South Africa in February 1966 for a two and a half year spell with the Arcadia Shepherds, in which he was the club's top scorer. He then returned to England when he signed on with Hereford United.