I have looked through my family tree and I do have a record of a William Appleton marrying a Hannah, however the marriage date is 1859. The strange thing about this marriage is that Hannah's maiden name was Appleton as well therefore it was most probably a cousin of some kind.
I am sorry that I have not been able to provide a link to your family....where abouce where they based. It seems that my whole family were based in Beech Hill, Tadley, Strstfield Saye area. If you ahve any 'Appleton' ancestors from these areas then it is most probably that my family is related.
Let me know if you think there may be any further connections.