I just came across a version of "Britania's Disgrace" or "Dying British Sergeant" from a journal entry dated August 28, 1799. If the dating by the author is to be believed (no reason to think it shouldn't be), this would seem to be the earliest known reference to the song. It comes from the journal of one James Tinker, living at the time in New London CT and brought to Western NY to the town of Henrietta in the 19th century.