Just fort I'd put me two penneff worth in.

The song may be late Victorian and alludes to the fact that the infant bodies of the poor were often put into the sewers in East London. The song probably came off the streets and worked it's way into the Music Hall. The Oxford Complete should give the earliest recorded use of the song although the phrase itself is much older (a MOTHER'S LAMENT.

I have yet to see an 'authentic' Lyric and there seem to be several popular versions. There is a version that is gender neutral in that "He" becomes "It". This may not seem so perverse as attitudes to child deaths amongst Victorians were very different because of the very high frequency they occured and particularly within the poorest communities.