Hi Keren,
You're welcome

This looks like Florence in West Auckland in 1881 with parents John (a farmer) & Elizabeth - again this is free-to-view on ancestry or familysearch etc
RG11/4926 Folio 72 Page 75
and same family in 1871:
1871 RG10/4887 Folio 32 Page 1
School Aycliffe, Durham
BARLOW
John head m 41 Farmer of 120 acres Stapyleton Yorkshire
Elizabeth wife m 40 Farmer's wife Gilling Yorkshire
Margaret dau 19 " dau Darlington Durham
Anne " 17 " " Westerton "
William son 15 Scholar Darlington
Sarah dau 12 " Coundon
Paull son 10 " Merrington
James " 8 " School Aycliffe
Elizabeth dau 7 " "
John son 5 " "
Joseph " 3
Florance dau 11 months "
I'll leave both families there until you get William & Minnie's marriage certificate to confirm parents, please do come back with the details and then we can go further back.
I see you have another post asking about John Wyatt, mentioned in your first post, it might be as well to make a new separate post about the Brettell/Cartwright families and keep this one for the Kilburn/Barlows to avoid any confusion - if you post details of what you've already found out about them it will save any duplication of searches
Kind regards, Barbara