Not many generations. Snopes thinks this idea dates to a book by James Leasor, The Plague and the Fire (1961).

Well - I was born in 1961 and we were taught it as fact! I suppose in popular culture a generation is only three years or four years; and I still meet people today in education who are only too happy propagate the plague myth, just as many people believe the Green Man to be pagan.

There is folklore, there is fakelore; happily there is QI as well, who delight in pricking this sort of thing, like the old Camel and the Eye of the Needle and other myth-conceptions, which we might pass of as folklore if we're feeling generous.