Hi Les in Chorlton,
I have Harry's Folk Songs & Ballads of Lancashire in front of me now, open at the Cob-o'-coalin' song. If it is the same book that you are referring to, it says,the words and tune are traditional, arranged by Harry. 'To this day children in the Oldham area sing a shortened version of this song and collect money for fireworks.' The book was published in 1973, so the latter comment may no longer be true.
I remember Harry singing this many a time while I was a member of the Unicorn Club in Church Street Manchester. If my memory serves me right, he said he learnt it as a child in Failsworth. IMHO it has all the elements of a vestigial pace egg song with a bit of the surreal thrown in ( the umbrella & pepper pots). Typical of kids!
All the best.
Mary Humphreys