I think I first came on the reference to Black Velvet Band originating in Barking in a book by Dave Occomore. It isn't the song we know now but is recognisably the same. It is also the earliest recorded occurence. There may have been earlier versions.Barking was a very important seaport although it has been eclipsed in size by it's suburb Ilford. I read somewhere that about 70% of England's fishing catch was landed in Barking during the middle ages.
Limehouse seems to have moved about a bit during my lifetime. When I was young it referred to the area just west of Poplar - ie. the old Chinatown. Now it seems to have moved further west no doubt due to renaming Stepney East station. Just south of this station is Ratcliffe which is hardly remembered as a separate area now - Ratcliffe Highway is now just The Highway.