at the top of the page, under 'quick links', you can find "Bruce Olson's web site", a scholarly study of old songs by a man who died a couple of years ag...now hosted on Mudcat

from this I found:

"In Scarlet Town where I was bound/ ZN1459| Barbara Allen's
Cruelty/ Tune: Barbara Allen's Cruelty/ Licensed according to
Order/ RB3 434 [two copies] = CR 675: BDBB [HH1 11, HC 652,
653] [CB p. 173. Child ballad ZC84|, Roud ZR54|. Cf. N1756,
N709. Pepys in his diary mentioned Mrs. Knipp's song of
"Barbery Allen" on Jan. 2 1666. This earliest copy is, however,
considerably later] "

I'm sure it was recorded early in the 20th century, as it was always popular....we will see what others have to say.