Hell, the plague hit London in 1665 (that and the Great Fire in 1666 are well remembered dates for all British schoolkids). We tend to look at recent history as anything after the Norman Invasion (1066 - another easy to remember date).
I did check my sources, only to find the main reasons for dispute were less about the age of the rhyme (but I know I read that somewhere) and more because the rhyme has versions all over the world and the plague interpretation only surfaced after WWII.
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