The best information I've found on this so far is from Lesley's site:
"This appeared in English County Songs (1893) under Songs of the Sea. It had been printed previously in a collection of southern country songs, Besom Maker and Other Country Folk Songs (1888) by Heywood Sumner. Broadwood states that in printed versions the A appears as A sharp in bars 4, 8 and 14, but she altered it to natural A, as that was "possibly the older form of the tune." Rev. Baring-Gould also collected the tune. It was printed on broadsides which is listed in the Charles Sanderson catalog.
The song was popular in Britain, Ireland and in Wales."
Now, this may well have been composed - as Levy says - by W. J. Florence around 1859. However, it seems quite possible to me that, since it was being collected in different modal versions as early as (some time before) 1888 in fairly far flung parts of the English countryside, there may be more to it than that. After all, it's not new to claim a song as your own, especially when you think you may get away with it.
More to follow, I sincerely hope.