There would not exist a birth certificate as civil registration was not introduced until 1837 but on the marriage certificate the father's name and occupation are normally shown, sometimes 'deceased' is also shown if that was the case. Also as you appear to have a year and place of birth you could search the baptism records including the non conformist records see under 'Church Records' http://www.genuki.org.uk/big/eng/DEV/Branscombe

For a copy of the marriage certificate see https://www.gov.uk/order-copy-birth-death-marriage-certificate