The above song is on DT (click), but seems to have no forum references whatsoever. They have left out the very best verse, which goes:

Three men went a- hunting
And something they did find.
They came upon a toad-frog,
And that they left behind!
Well, the Irishman said t'was a toad-frog,
The Scotchman, he said "nay"!
The Welshman said, t'was a jaybird,
With the feathers worn away!

(As sung by NCLR, vol. III.)
I had always understood this to be a Welsh song.