From what I gleaned when researching this song, the tune was written by members of Willard's Leap. The words appear in Yorkshire Anthology: Ballads & Songs Ancient & Modern (p. 418f.) edited by Joseph Horsfall Turner, 1901, where they're attributed to Matthew Harman of "Scarbro'". I would have sworn there was an earlier thread about this song, but I'm unable to find it with either Mudcat search or Google.

Terrific rendition by Jeff Gillett and Ron Taylor on their album Both Shine as One.