Here are the liner notes, copied from Artisan's website

DEAR MATHILDA
This song was given into our keeping by the late Tom Brown, a traditional singer from East Anglia. Having no children to sing his songs, Tom parcelled them out to friends to keep them alive. (Trad. arr. Bedford with additional verse by Brian Bedford) Vocals – Artisan

Breezy, are the lyrics you've posted complete? Your remark "before I go any further" seems to imply there is more.

This is a very odd song to be called "traditional." It doesn't seem to have a regular rhyme scheme or metrical structure (but then, I don't know the song; I only have the posted lyrics to go by). I wonder if it could be an old music hall song?

And Steve, why aren't Canada geese considered real geese?