Hello Eilleen
Unless Ann / Annie Moore is hiding and still to be found in the 1861 Census (with her Dad / Mother or with Relationship stated to the Head), or find her registered Birth or a Chapel Birth/Bapt record, I think you are going to struggle.
Ellen Jessop (Present / Witness) on the 1875 T. C. Exton = Annie Moore, Marriage. We have also presumed (presumptions always risky) from the 1875 Marriage Cert that her Father and Occupation at some point, was correct.
So I looked for Moore = Jessop marriages (before 1875), but came up with this 15 yrs later with a Gosberton link.
I'll post it, but this Wm Moore (below) is too young to be Annie Exton's Dad and I don't feel it helps

with Annie Moore's family of Moore:-
1900 Marriage, Pinchbeck, 4th July
Luke Jessop, 22, Labourer, Gosberton, Dan'l Jessop, Labourer.
Maria Moore, 18, Spinster, Pinchbeck, William Moore deceased, Labourer.
Present:- Edward Wilford ; Eliza Wilford.
1901 Pinchbeck
Edward Wilford, Head, M, 57, Road Labourer, Lincs., Wrangle.
Mary Ann Wilford, Wife, M, 44, born Wrangle.
Maria Jessop, Daur, 18, born Lincs., Fishtoft.
Luke Jessop, Son-in-Law, 23, born Gosberton.
David J E Jessop, G/son, 5 months, born Surfleet.
Plus 2 Visitors.
Not looked at G/son and couldn't find a first marriage to see if Mary Ann Wilford was married before / previously Moore.
1883 Maria Moore, Birth Index (f m p), Mother M. Surname: Evison, Reg. District Boston.
1882 Marriage, Fishtoft, May 17th
William Moore, 25, Bach, Labourer, Fishtoft, John More.
Mary Ann Evison, 24, Spins, Fishtoft, Rich'd Evison.
Present: David Moore ; Susanna Moore

Mark