The difference between an 18th century stage song which has been absorbed into the tradition and a 19th century music hall song is that this process has not had time to work on the latter.

Sensible post all round, Howard, and the above is true but not necessarily the whole story. I don't claim to be any kind of an expert, but my understanding is that Music Hall compositions were using new tricks like chromatic melodies and modulation, which weren't a part of those older songs.