The Black Plague entered (well, re-entered) Europe in the 14th century; outbreaks continued from time to time right up into Tudor times (Shakespeare managed to survive his toddler years, perhaps by having been kept indoors, the Pestilence took a lot of people in Stratford).
Yes, and on further research, I learned that the main family estate was on land near a village in Oxfordshire that had been completely decimated by plague around 1490. Only 10 percent of the population survived and they had all moved away. Which I guess was good for my peeps, as they moved in around 1570 and built a pretty large manor house.