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