Ah, those compilations! Lloyd was Carthy's immediate source, though, and had recorded the song himself in 1956 or thereabouts. Although (see above) Lloyd said he had found a text "in a Vauxhall Gardens songbook of c.1770", I've still not come across any other reference to such, though it certainly did appear on broadsides and in chapbooks from the mid-18th century onwards. It's likely that Lloyd re-wrote the words himself from printed and traditional sources, setting them to a tune that Maud Karpeles found with the ballad in Newfoundland, again modified by himself; so a partial writer's credit is fair enough, though it's a pity that he wasn't more forthcoming about his own interventions.

There are two sets of the song from genuine tradition (both Newfoundland) at folkinfo.org:

The Bloody Gardener
The Bloody Garden