My suggestion would be to purchase the marriage certificate for Frederick and Sarah Ann - December quarter 1882, Registration District Newcastle L, ref: 6b and page 141. The marriage was a civil marriage (register office possibly) and this will give you both Frederick's and Sarah Ann's fathers' names. As you say, there are no births registered in 1865 in the appropriate place - although Biddulph did come under Cheshire until 1894, rather than Staffordshire.
