GerryM wrote: Recorded by many, usually called Little Brown Dog, possibly arranged by PP&M, unlikely to have been composed by them.

Possibly they claimed an arrangement credit (after all, they were a Sixties Folk Group, and that's what Sixties Folk Groups did). But they assuredly didn't write it. Steve Gardham cites a broadside copy that appears to be nineteenth century although it has no precise date. The Journal of American Folklore printed a copy in 1891, which is the oldest copy I know which can be precisely dated.

Both "Autumn to May" and "Little Brown Dog" seem to be relatively modern names. But there really isn't a generic name; it's known by all sorts of titles: "When I Was a Little Boy," "Speculation," "As I Set Off To Turkey," "The Lofty Giant," "To London I Did Go," "The Liar's Song," many, many others. Probably the most common is "When I Was a Little Boy" or variants thereon. It's known throughout Britain, most of the eastern United States, and most of eastern Canada.