Wood was born in Winsford, Cheshire and attended Meadow Bank School in Winsford Village. As a youth he played football for Whitegate Victoria and Winsford United, before turning professional with West Bromwich Albion in April 1928. He made his Albion debut in September of the same year, in a Division Two match against Notts County. He went on to make 281 appearances for the club, scoring 66 goals, and was part of the Albion side that won promotion to the First Division in 1930–31 and beat Birmingham 2–1 in the 1931 FA Cup Final.