"The song was definitely sung at the London pleasure gardens in the middle of the 18th century and that is its likely origin"
Why?
The theme is timeless, as are those the motifs of all folk songs
Your two-way suggestion for the origin of folk songs seems to have gone by the board Steve and we are back to the folk never having produced anything for themselves
What an uncreative, unimaginative people the English seem to have been!

Jim Carroll