Very sad to hear of Bill's death. His 'Oller Boller' reminds me of my Dad, (W'ton born and bred) who remarked that 'kids don't play in the streets any more', going on to talk about the games Bill recalls, in a similar accent.
Regarding the lyrics - a distant cousin of Bill's has posted, below a YouTube post of Bill singing 'Oller Boller', that their 'Aunt Mil' is mentioned in the original. Could this mean that 'Hardmill's Shop' is actually Aunt Mil's shop?