Although the earlier broadside song has occasionally been found (chiefly in America) still in oral currency, the song popularised by the Copper family -the one that most people are thinking of when they refer to Babes in the Wood- is a relatively modern thing, having been made by William Gardiner (1770-1853). It was widely published: sheet music (uncredited and undated) can be seen, for eaxample, at the Lester Levy Sheet Music Collection:

Sweet Babes in the Wood. A Ballad. Founded on the well known Legend. Philadelphia: B. Carr's Musical Repository, n.d.

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