Mrs Verrall's song derives from a broadside ballad of the second half of the 17th century, The Two Faithful Lovers. Three editions can be seen at Bodleian Library Broadside Ballads:
The Two Faithful Lovers
The tune to which it was set was Franklin is Fled Away; this derives its name from A mournful carol: or an Elegy lamentating the tragick ends of two unfortunate faithfull lovers, Frankin and Cordelius, he being slain, she stabb'd herself with her own dagger. To a new Tune, called, Frankin is fled away, which was licensed to William Gilbertson in 1656. Gilbertson's edition can be seen at the Bodleian website:
A mournful carol...
Franklin is Fled Away
More detail on the tune and the various songs set to it can be seen in Claude M Simpson, The British Broadside Ballad and Its Music, New Brunswick: Rutgers University Press, 1966, 232-235. Simpson reproduces the melody as printed in Apollo's Banquet for the Treble Violin, 1670, No. 67, where it appeared as Francklyn:
(Original a fifth higher)
Another version of the melody appears in D'Urfey, Pills to Purge Melancholy, 1719-1720, vol V, 129, where it is called O Hone, O Hone, and accompanies a short song parodying Franklin, titled A Ballad, made by a Gentleman in Ireland, who could not have Access to a Lady whom he went to visit, because the Maid the Night before had over-laid her pretty Bitch.
O Hone, O Hone