I know this song from my grandad a broad geordie and my gran a broad glaswegian and another song to the same tune both in a heavy geordie accent.

My poor baby's gone down the plughole
My poor baby's gone down the drain
The poor little mite, what a terrible sight
He ought to bathed in an old corned beef tin

the other being

My Bonnie lies over the ocean
My Bonnie lies over the sea
My bonnie lies over the ocean so bring back by Bonnie to me

Also learnt the second one at Pelaw infant school in 1993