We used to sing that song with the kids in nursery school thirty years ago (I didn't realize it was that long ago, till just this second--I thought, yeah, twenty, then I did the math!!!) No one knew where it came from then--though our general sense was that it wasn't that old(we were only 18-20, and none of us had known it as children--

It seems odd that, peculiar as the lyrics are, they should have been passed down through at least one and a half generations, and circulated god knows how far, with very little alteration--