The original tune was never recorded or written down. In fact all known variants can be traced back to Bell's Ancient Poems Ballads and Songs of the Peasantry of England, 1857. In his notes Robert Bell says of the tune, 'There is a marked resemblance between it and a song of the date of 1650, called 'A Cup of Old Stingo'.' This is easily accessible and appears in, amongst others, Chappell's Popular Music of the Olden Time Vol p308. I'm sure it will be found easily by Googling it.

You say you are interested also in modern tunes used for it. I know Ray Black of Harrogate has used a tune for it. If you pm me I can give you his email address.