Not usually, I think, though the metres are much the same.

Child made no reference to the song that I recall. The putative connection to The Two Magicians was floated by later scholars. Bronson thought a derivation "very probable". Most of the examples he quotes are from the West of England, with one Irish example (without words) from Petrie. Related or overlapping songs (Sally My Dear etc) were common enough, and found mostly in England and New England; occasionally in Canada and Ireland. No sign of any Scottish examples so far as I can see.

Hall and MacGregor certainly used the set Sharp got from Louie Hooper and Lucy White, as Mary suggests; probably they got it from one of Sharp's books, but there may have been an intermediate revival source, as "beat them bushes" appears to be a modern alteration of "bang the bushes". Steeleye Span, too, recorded an arrangement of the Hambridge set (though they acknowledged no source in their sleevenotes) so it's hardly surprising that the words are essentially the same. The song did the rounds of the folk clubs quite a lot in the late '60s and early '70s, commonly with extra verses added from other sources, or made up to the same formula.