Spink began his career with Writtle Minors F.C. at junior level before going as a school boy to West Ham United, but soon moved to Chelmsford City and then, at the age of just 18, to Aston Villa. It was almost five years before his big break in the first team came along, and it came on the biggest stage of all – the European Cup Final. Ten minutes into the 1982 final against Bayern Munich, Villa's first choice goalkeeper, Jimmy Rimmer, was injured and substitute keeper Spink was called into action, having only made one previous appearance in the first team. Spink performed superbly, keeping a clean sheet, and Villa won the game 1–0. By curious coincidence, Spink and Rimmer are two of the four England goalkeepers with the shortest international career (45 minutes).