The copyright date is 1939 but I think (alas, can't go on oath) that I can remember it being sung at parties some years before that. Can anyone confirm? I've always suspected Weston and Lee of doing the occasional bit of quiet recycling of 'things heard', a suspicion that is hardened by the fact that the sheet music has verses inferior to those usually sung. The sawing off of M.Brown's legs does not occur in the printed version (not the one I have, anyway) but was always in the first verse of the party song (and dance) which also always had the 'Give it to the girl next door' verse (give what exactly?) and concluded with 'Oh my what a rotten song'.

Why did the lady need to lift her knees?

Knees up Mother Brown
Your drawers are falling down...