Chris Foster sings a version of this song, which he calls "The False Knight". His is longer, and verses about a cat and a parrot named Polly are included. I think that the parrot warns her, and the parrot is promised a nice cage with a door of ivory for his services. (Well done, well done, my pretty Polly). It's on Sting of The Tale. I will try to transcribe it if I can make out his accent, as the tape has no lyrics with it. Some of the verses are as posted above.

The song bears no relation to The False Knight On The Road, which is a song about a little boy or girl confounding a riddling knight.