This series of songs was a mishmash long before it got across the pond.
The main stock of stanzas utilised appear in at least a dozen broadside ballads in some form or other, and about half of these entered oral tradition. The broadside hacks used the stanzas willy nilly for this popular theme of the camp follower.

By the main stock I mean 2 & 3 in the guest posting along with about 3 or 4 others, oh and Masato's stanza.