I believe the original or at least earliest is Irish, but not the Republic. It used to be called 'The Strands of Magilligan'. It came over very likely via Liverpool then Manchester. By the time it reached the south of England the broadside hacks and oral tradition had changed it into 'The Streams of Lovely Nancy'. It's interesting to trace the printed progression from Northern Ireland to the south of England in the early 19thc. But it's useful to know that it spread into the Republic as well.