The tune for the broadside "Bellman" text was "O man in desperation", which was popular from 1585 to nearly 1600. See "Jerusalem, my happie home", 1587, in the Scarce Songs 1 file on my website for that song and some possible tunes for it. There's nothing to suggest that 19th and 20th century tunes for it are of any great antiquity. [Extracts of it are still in some current hymnals]