I have heard that the tune is traditional Welsh, and that Henry wrote the words for Ann Boleyn, who did not, to the best of my knowledge, have three boobs. I have also heard that the set of words "What Child Is This?" was written when Elizabeth I wanted to use the tune for a Christmas service, possibly in honor of her mother.
A harper friend of mine, finding her Renaissance Faire set unexpectedly usurped by a christening on the same stage, sat quietly in the background and played "What Child Is This?" for twenty minutes.