Storer was a specialist wicket keeper who was reputed to stand up to the wicket against fast bowlers. He was also a highly skilled batsman at a time when wicket-keeper batsmen were rare and twice averaged over fifty in a season. His first-class record of 216 not out came against Leicestershire in the 1899 season and he was the first professional to score two hundreds, against a strong Yorkshire side, in a match. He was also a competent leg spinner, taking 232 first-class wickets at 33.89. Storer also appeared for London County.
Storer toured Australia for England, making his debut in the 1897 Test at Sydney and played against the tourists at home, his last Test coming at Trent Bridge in 1899 when he was also named a Wisden cricketer of the year. His Test appearances were limited by the selectors preference for Dick Lilley.
Storer was ‘serverly reprimanded’ for ‘objectionable language’ during the 1898 test where he was overheard to say “You are a cheat, and you know it”, during the luncheon on the final day of the 5th test match at the Sydney Cricket Ground.