I think that you will find that at that time it was not called music hall, but performers performed at "Smokers".
Much of my collection of music hall books has been sold off to other collectors but I still have several. One that might be of help to you is "Sweet Saturday Night" - pop song 1840-1920 by Colin Macinnes published in 1967 by Macgibbon & Kee. You might try looking for a copy. The Ballad of Sam Hall is one song that goes back to around this time and maybe even further.

Happy hunting.