There are a further two sets in the DT besides those George mentions above:

BARBARA ELLEN (3)  With tune; noted by Cecil Sharp; the DT file does not say where, when or from whom.
BAWBEE ALLAN  With tune; transcribed from a record by Ewan MacColl.  Traditional source not given.

So far as the placename is concerned, Robert Bell (Ancient Poems, Ballads and Songs of the Peasantry of England, 1857) comments:

"In Percy's version of Barbara Allen, that ballad commences "In Scarlet town," which, in the common stall copies, is rendered "In Redding town."  The former is apparently a pun upon the old orthography - REDding."

While that is not impossible, it should be noted that the "stall copies" referred to are all later than the texts in the Reliques.  Chappell (Popular Music of the Olden Time, 1859) added:

"It has been suggested that for "Scarlet" town... we should read "Carlisle" town.  Some of the later printed copies have "Reading" town."