My Hopkinson family is from East Retford, Nottinghamshire. The info I have starts in the late 1700s. Francis Hopkinson was born about 1751. He married Mary Nettleship in 1782 and they had 9 children. None were cloth dyers, though. Some were auctioneers, some were printers.
The name Francis has been carried on in the family right down to the present generation.
If you think there might be a connection, please get in touch.