One other side note:
There is apparently a reference to the song in Chapter 9 of Charles Dickens' "Martin Chuzzlewit" (1843-44).

Referring to a young lad who turns up at Mrs. Todger's boarding house:

"At the period of which we write, he was generally known among the gentlemen as Bailey Junior, a name bestowed upon him in contradistinction, perhaps, to Old Bailey, and possibly as involving a recollection of an unfortunate lady of the same name, who perished by her own hand early in life, and has been immortalized in a ballad."

See James T. Lightwood, "Charles Dickens and Music," Chapter 6 for a brief discussion, but no new information.

Regards,
John