I'm very grateful to Bob for his rip-roaring lines: if this isn't what the chidren sang, it's what they ought to have sung!
The first part is virtually identical with a song which I know as 'In Leicester Town' that has the young man touching various other parts of the maid's anatomy - eg
I put my hand upon her toe/She said "Young man, you're rather slow."
I put my hand upon her breast/She said "Young man, now that's the best."
Whether this was indeed the song (probably in a cleaned-up version) referred to by Ransome we may never know: he gives only the title, and no further clue.
Tim