My Old Man's a Dustman, as sung by Lonnie Donegan, seems to be an amalgam of the J.P. Long song and My Old Man's a Fireman, which had been around long before - before Long, in fact. Donegan knew it as a kid in a parody form: "My old man's a dustman, he fought in the Battle of Mons ..."

I have written about this at some length
here but the oddest thing is that Leslie Bricusse is one of the writers credited with the song as sung by Donegan. He doesn't go into this in detail in his most recent autobiography but as far as I can make out he would done no more than tidying the gags which had come about during live performances.