Are you sure you have the right baptism?
The marriage is at Shadforth, 12 July 1845
Ralph Prest, father Joseph Taylor!!!
Ellen Patchet, father William Branson
Indexed locally in Durham as Ralph Prest/Taylor and Ellen Patchet/Branson
So his fathers surname is also different?
From FreeReg, another possible baptism -
19 May 1825 at Pittington St Lawrence
(daughter of) Anne Patchet, Singlewoman
Ralph is in Witton Gilbert in 1851 with daughter Elizabeth. Widowed. So you don't have details for Ellen, age and birthplace. from that census.
Burial, 5 August 1850 at Witton Gilbert
Ellen Prest, age 26
(from Family Search)
The Eleanor, daughter of John + Eleanor, was bap 10 June 1827 Chester le Street? They appear in the register as married, Patchet in the surname column. His occupation is Wagonman. Abode Fatfield....
John + Eleanor are having children baptised there from at least 1819. They appear in the 1851/61 census as Padget.
A possible marriage?
7 March 1848 Chester le Street
Eleanor Paget, father John Paget
1851 census - Elenor Trotter, 24, born Fatfield, wife of George