John Foreman used to sing lots of cockney and music hall songs, including

The Ratcatchers Beautiful Daughter
The Coffeepot song (All I want is a proper cup of coffee...)
Villikins and Dinah
The cockney alphabet (spoken) starting
The Old Dun Cow
A is for 'orses
B for and after
C for yourself
E fer Brick (Heave a brick)
G fer Police (Chief) etc
One about whitewash (Slap dap? - don't know the name)

There are also a lot of others in the Bodley collection.
All Around My Hat was originally printed in cockney dialect of the time, where W and V were interchanged (as in Villikins), as were many other songs.
The Black Velvet Band originated in Barking, just east of the Cockney area, not Belfast