All I know is that my father used to sing these lines when I was a boy in East London (i'm now almost 70...)
"The black cat piddled in the white cat's eye...the white cat said 'cor-blimey'..the black said 'you silly old sod,you shouldn't have stood behind me"...so when it started and where from I don't know....but it's certainly in excess of 70 years old..
             He usually followed it up with another 'song'.."please don't pull our lavatory down....etc"...