I don't think that Martin made up the tune, though he certainly modified it rhythmically and recast it into a modal form. A lot of people who didn't read his notes are probably now repeating it as something genuinely traditional. I seem to recall (though I don't guarantee that I remember correctly) his saying that he felt he might have gone a bit over the top with some of the material on Shearwater.

For information on Henry My Son, and its "Cockney" music hall form, see other threads here. It isn't really relevant to this particular discussion.