Come now, Peter Kirker, it's a pretty good song, isn't it? And considering it is a commercial music hall number, written by no one of note and sung by no one in particular, it is quite remarkable that it is still current and fairly widely known after 117 years. And I've seen and heard it work on a modern audience.
Kilgarriff notes that authorship was claimed on both sides of the Atlantic in 1888. The American J J Sullivan certainly sang it, but the credit (or blame, if you prefer) for the song probably rests with Rolmaz and his London publishers Francis Day and Hunter.