Storey played for Ardsley Welfare and Grimethorpe Athletic in non-League football while working as a miner, before joining Huddersfield Town in 1943. After leaving them he played for Wombwell Athletic before moving to York City in 1947. He played for York in the FA Cup semi-final in 1955 and left a year later after making 354 appearances to join hometown club Barnsley. He later had periods with Accrington Stanley and Bradford Park Avenue before returning to York as trainer-coach for three years.