I think it's one of the spin-offs to Arthur Lloyd's 'Married to a Mermaid' 1866. His own follow up was similar to this The Man at the Nore' 1866

MtaM starts 'Twas in the broad Atlantic'
MatN starts 'Oh, my father he kept the Eddystone Light'
The Merman certainly predates 1873 which is when it was printed by Glasgow Poet's Box. It is of course also in Laws as K24.

The chorus as you all know is taken from later versions of the Baffled Knight and was also used for various shanties and sea songs.