Raph's book is a better than average compilation of popular tunes, but not a source of accurate information.
The Contemplator Bibliography lists several of these collections, Song Treasury, Fireside Book of Folk Songs, etc., the notes often from anecdotal or unverifiable sources.

Fuld* quotes Chappell. He notes that "The melody is also said to have been known as 'Brighton Camp,'; however no earlier printing of it has been found under this title, and the 'Brighton Camp Quick March,' entered in Stationers' Hall on Nov. 12, 1792, has a completely different melody; BM." (BM- British Library, British Museum)
At the beginning of his notes, he says, "The earliest known version of the melody was printed about 1810 in Hime's "Pocket Book for the German Flute of Violin" (Dublin, n. d.), vol. 3, p. 67, under the title "The Girl I left Behind Me; NLI." (National Library of Ireland, Dublin)
* James J. Fuld, 3rd. ed. 1985, "The Book of World-Famous Music Classical, Popular and Folk, pp. 242-244, Dover Pub.

Does anyone know where the 'Brighton Camp' statement first appeared? It would be useful to know how the citation started since it has been repeated in a number of publications. Here is an example:

folkinfo.org- 'This lively traditional fife tune, imported from England as 'Brighton camp,' was known in America as early as the seventeenth century, and became generally popular during the Revolution.'
They go on to say, however, the firsy Brighton Camp was formed during the French invasion scare; .... 1793...." Fuld (above) is quoted.

"The Brighton Camp Quick March" is listed with "Early American Secular Music... at www.colonialdancing.org. as an import from England. I can't find any reason for it, but did this march and the Brighton Camp of the 18th c. (and its use during a French scare) somehow get confused with the French-Indian Wars of an earlier time?