Gibb
Smith's tune is note for note the sheet music, even in the same key!
The words are ascribed to AJC who I will try to identify. Kilgarriff gives the initials wrongly as ALC and states this is the pseudonym of Wm Makepeace Thackeray. It is definitely Thackeray's style (a la Little Billee) but he has got the initials wrong if it is. If it is WMT I would expect to find it in one of his books of ballads which I have somewhere. The sheet music says arranged by Michael Watson and Kil interprets this as MW wrote the tune which is not really the case.
It was published by H D'Alcorn in 1866. The cover is a famous one with Lloyd dressed as a sailor at the bottom of the sea greeting a pretty young mermaid.