Greg's date of 17th Century is much more likely that the days of the Black Death.

Is there any trace of the rhyme before 1800? Here is where our English friends may come in with more information. The rhyme has also been related to smallpox epidemics, the ring around the rosy being application of make-up to cover up blemishes.
Somewhere in Google is a story with a tie-in to Shiva and Hindu mythology, but that one is too far-fetched to quote here.