Signed by Charlie Paynter from Finchley, Tucker made his West Ham United debut in October 1947, scoring a hat-trick at home against Chesterfield.
Paynter allowed "his player" to stay at the club on the proviso that Tucker would sign professional forms with West Ham as soon as the season was over.
He finally became a first-team regular during the 1955–56 season, and was called into the England squad for a game against Brazil although he didn't play.
Tucker had a fractious relationship with manager Ted Fenton – he once went on strike over pay – and his feud lasted well after he had left the club.
He went on to play for Notts County after an acrimonious departure from the east London club in March 1957, although he still insisted on training at West Ham.