My mother used to sing this to me (don't a lot of these lyric requests start off that way?) and I'm missing two of the lines. Googling turns up none of the unique phrases, so perhaps someone else has this in their brainbox...

"Did you ever hear the story
Of the egg of ancient fame?
He'd a belt and he'd a necktie
But they both were the same."

...
...
He was charming, he was handsome,
Humpty-Dumpty was his name."

I'd also like origins and age if there are any results for this! I remember it going along with songs like 'White Coral Bells' and "My Pigeon House I Open Wide", if that helps...