Thanks, Masato. I had heard that the project to get Halliwell, The Nursery Rhymes of England, on to the Internet was getting well along.
They have completed the 4th edition, 1846 (447 kb), with the index and contents.
"Around the Green Gravel" is on p. 195 of this edition.
It looks like they are working on the 1st and 5th eds, indices at least may be available in the future.
Nursery Rhymes: Halliwell Nursery Rhymes Index

Masato, do you have the contents of the 1842 edition?
Still looking for more of the "Free Mason" changlings.