Mmmm ! Fishing on the Thames existed for many years, and I have no doubt nets were used, particullay when the Salmon ran befor it became a "Game" fish.
Though I suspect the emigrant theory may also have its place.
The Medway before polution steralised it was famous for its smelt fisheries by the Bawley Men as late as the 30's using nets above Rochester Bridge - as far as Alesford
Bearing in mind the Bawleymen fished the London River and the Estuary as far out as Margate and the Naze, I see no reason why there could not have been some cross polenation of song.
Sorry for any typo's, it's after closing time.