Freddy:
The "glorious mud" song (its actual title is "The Hippopotamus") is by Michael Flanders and Donald Swann. They are too late in time (1950s) and too upper-class to count as music hall.
"Daisy Bell, or a Bicycle Made for Two" is by Harry Dacre, an Englishman in America. It was written in 1892. It may well have made it into the music halls, but I don't know.
I have never heard "Proper Cup of Coffee", but it has all the earmarks of music hall.