Born in
Darfield,
West Riding of Yorkshire, Storey worked at a
W. H. Smith in
Barnsley, West Riding of Yorkshire at the age of 14 before becoming a
miner at Houghton Main Colliery. He missed one game for York during the
1947–48 season, making 42 appearances and scoring 12 goals in all competitions. An injury resulted in him missing the
FA Cup semi-final against
Newcastle United on 26 March 1955 and several league games, with many fans believing this cost the club
promotion, although he was able to play in the 2–0 defeat to Newcastle in the semi-final replay on 30 March at
Roker Park. He received a
benefit match in 1955 and was granted a
free transfer in 1956 after making 354 appearances and scoring 42 goals in all competitions for York, joining hometown club
Barnsley in May to run their
reserve team. He managed to play for Barnsley due to an injury to one of their
first team players and he was able to "demonstrate that his old skills had not deserted him". He made 29 appearances and scored four goals in the league for Barnsley before joining
Accrington Stanley in October 1957, where he "once more belied his age with some top class displays". He made 30 appearances and scored two goals for Accrington in the league and joined
Bradford Park Avenue as
player-coach of the reserves in July 1959. He made two league appearances for Park Avenue and following his retirement as a player he rejoined the York coaching staff as a trainer-coach.{{cite news ==Style of play==