This smacks of Max Miller, but it had a brief vogue roiund my way in about 1958:

Jack and Jill went up the hill
For a bit of hanky-panky.
Jill came down with half-a-crown--
Jack must have been a Yankee!

(Explanations available on request for puzzled Americans!)

There was one interminable ryhme from my early days in infant school (age 5-7), which I could never remember in its entirity. I have a feeling it was in a thread a couple of years back. I don't think I can recall more than the odd line now ... it starts off with someone's baby being ill, and goes through a long list of substitutes: "... couldn't come, So they sent for ...". Just grasped this from below the surface of consciousess: "... wasn't in, So they sent for Rin-Tin-Tin". (R-T-T was just giving way to Lassie in those days.) If you know the whole thing, you could make an old man very happy (or just very old!).

Steve