There may be more info in the Great British Song Book, but my copy has gone awol again. If I find it, I'll let you know. I do know that at least one version has bathing instead of washing, pronounce "barfing" - perhaps that's why it changed....Funny, we were only singing this to the SOS (Spawn Of Satan - don't even ask) the other night - she likes the tune, but is far too ..... robust.... to go down the plug, unless it is one of those on the Hoover Dam....
Best sung in a Dick Van Dyke cockney accent - as in: moy bie-by as gorn darn ther plahgole, moy bie-by as gorn darn the plahg.....
LTS