One I only just realized: Adam Macnaughtan's "Jeely Piece Song" uses the tune of "Does Your Chewing Gum Lose Its Flavour On the Bedpost Overnight?" which I used to attribute to Lonnie Donegan.

Google finds it credited like this:

Based on the 1924 original by Ernest Hare & Billy Jones
"Does The Spearmint Lose Its Flavor On The Bedpost Overnight?
(Marty Bloom / Ernest Breuer / Billy Rose)"

Are Ernest Hare and Ernest Breuer the same person?
Was Billy Jones a pseudonym for Billy Rose?
Where did Marty Bloom fit in?
And where did Donegan find it?