Then there's the nursery rhyme, probably unrelated:

Hickory Dickery Dock,
Three mice ran up the clock,
The clock struck one
and two escaped with minor injuries.

On a more serious note, I've heard semi-plausible cases made for supposed ancient meanings embedded in some of these songs, but given a little time to think about it, they just don't feel right. Like the London Bridge song. I heard a case made for it on the History Channel the other night, but he was just repeating what he'd been told, they didn't actually provide photos or sketches or early print documents to somehow bolster the story.

SRS