I'm not absolutely sure that what is on that 'Rhymes.org.uk site is a 100% accurate. I suggest that you have a look at the books of those who have carried out research in this subject ie Peter and Iona Opie. Jeremy Barlow has also done some work in this field and some time ago he did a programme about it on Radio Four. Iona Opie also participated and of course they played some of songs performed by the Broadside Band from their CD Old English Nursery Rhymes. It's also worth pointing out that in the sleevenotes of that CD, quite often references of possible or not so possible origins of the rhymes are given. Sadly, they say that a lot of nonsense has been written over the centuries on this subject. Yes and of course Ring-a-ring Roses predates the Plague and is possibly German in origin.