I have sung this since my long past schooldays, never really questioning where it came from, just enjoying the song, which I think echoes Jim's point.
Yes, it's interesting to research origins, but only up to a point. I did look into it the other week, when the BBC featured some project about English folksingers going into a forest somewhere in southern England to play and sing along with nightingales at silly o'clock am. The instrument they took with them was that very traditional English one, the shruti box!!
We don't have nightingales in Scotland, but some pretty tuneful warblers!