I'm thinking players like Botham, Gower and Gooch would have won in all of 1977, 1977/78, 1981, 1985 and 1986/87. (Turns out it was actually just Botham that played all of these)
Edit: Having a look the 19th century players have this sewn up because of how many series they played back then. Billy Barnes played 21 Tests in his career and he won the ashes 7 times from 1882-90.
Edit again: Barnes is tied with Bobby Peel, Arthur Shrewsbury and Walter Read for the record seven wins. All 1880s players