The Lonnie Donegan version seems to have evolved from what I assume is the original written in 1922 by JP Long, E Mayne and A LeFre:

My old man's a dustman
What d'yer think of that?
What d'yer think of that?
What d'yer think of that?

He wears a dustman's trousers,
He wears a dustman's hat,
And he talks a dustman's lnaguage,
What d'yer think of that?

When they only paid him thirty bob a week,
He called me his little "Turtle Dove",
But since they've raised his salary to Four Pounds Ten,
He throws his rubbish where he throws his love!

The tune is different but sort of very loosely related in a cheerful cockney sort of way.

LFF