The Butler Metropolitan Theatre Songster was a DeWitt joke book. With that in mind, here is an American circus-minstrel-vaudeville spin on it:

"There was once a bold Fisherman,
Who sailed forth from Billingsgate,..."

Today it is (mostly not) known as Billingsgate Shoals but in the 1870s, before climate change was cool, it was the fishing village of Billingsgate Island, Cape Cod, MA, USA.
[41°52′14.30″N 70°04′07.0″W]


"But when he arrove off Pimlico,
The wind it did begin to blow..."

'Pimlico' could mean Baltimore, MD or a corruption of Pamlico Sound, which was more noted for its storms in the 1870s (Cape Hatteras &c.)
[35°15′17″N 75°31′12″W]