Here's the Chappell quote from "The Ballad Literature and Popular Music of the Olden Time: Volume 2; by W. Chappell 1859

BARBARA ALLEN.

Under this name, the English and Scotch have each a ballad, with their respective tunes. Both ballads are printed in Percy's Reliques of Ancient Poetry, and a comparison will shew that there is no similarity in the music. It has been suggested that for "Scarlet" town, the scene of the ballad, we should read "Carlisle" town. Some of the later printed copies have " Reading" town.

In the Douce Collection there is a different ballad under this title,—a Newcastle edition, without date.

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

Richie