I never realized before that there is an entire subdatabase (are you listening, Greenhaus? ... see French folksongs thread ... :) ) of folklore about folksongs. The fact is, we can't tell whether Henry VIII wrote it. He could have, but if so it's likely there would be documentation, if only because he would have wanted to brag about it. But it's the kind of story that gets around very well because it has appeal. I once read that Loch Lomond was written by a Scot who was about to be executed, but that turns out to be pure fakelore.