Roy Palmer published a version in his Room for Company. It is exactly the same text except Weyhill (Hampshire) is given instead of Howden. He got his text from Addison 'English Fairs and Markets', 1955. Not being aware of the Howden version Roy set it to the tune of Slaidburn Fair from Kidson's English Peasant Songs. I'm not much cop at sight reading but the tune he gives could well be a variant of ND.
It's many years since I sang and researched this song and I have a sneaky feeling it was published on a broadside with just a gap for the placename so that it could be sold at any fair and the singer could insert their own place name. i.e., '------- Fair'
If there was such a broadside (which is very likely) it would seem to date from the late 18thc/early 19thc. Certainly 'Nancy Dawson' was a very popular widely used tune then.