For more detail (which I didn't know about back when this old thread was new; some of my comments made here in '01 and '02 were therefore misleading or wrong), see notes to 'The Nobleman's Wedding' in the revised edition of  Marrow Bones. Most of the missing links were supplied by Steve Gardham.

Ansell and Valentine's costermonger song 'All Around My Hat' (c.1834) wasn't made from whole cloth, of course. It was a parody of 'Green Willow' (and other titles) for which see  Bodleian Library Broadside Ballads:

[The] Green Willow / William & Phebe

This itself, though in that form not much older than the parody, was partly made up of recycled older material.