Out of interest why John and Mary Pickering rather than the John and Margaret Hedley option , what makes it more likely as there is no baptism fot Jacob. Although it is quite possible that the 1830 baptism may have been him just getting baptised late.
I have also just spotted a new entry on FamilySearch, I knwo marriage certificates say his father was John
residence: Heworth, Durham, England
parents: Phillip Allen, Mary Allen
name: Jacob Allen
baptism date: 10 Apr 1815
baptism: Heworth, Durham, England
Dave