Just to add a bit more about John Hall's birthplace. Near to the Houghton (Blackburn) is a place known locally as Houghton Bottoms. There used to be a water powered cotton mill there years ago. This would have needed a reservoir or lodge to supply water to the wheel - could John have come from this part??
That makes things interesting. on the baptism for John Hall in Blackburn which states place of birth as Houghton his fathers occupation is a miller, this would go along with what you were saying about the mill.