Hi Joan:
Don't know if you're still searching for where this family ended up, but I found the following (whilst looking for a different Gray family):
1911 Census: James (born in Bell Quay) & Sarah Gray at 11 Florence Street, Winlaton, Durham (with son William & grandson Wilfred).
1901 Census: James (born in Bell Quay) & Sarah Gray at 11 Florence Street, Winlaton, Durham (with sons Robert & William and grandson Wilfred). Reference is RG13, Piece 4763, Page 44
1891 Census: James (born in Bell Quay) & Sarah Gray at Queen Street, Brandon, Durham (with daughters Mary & Jane and sons Robert & William). Reference is RG12, Piece 4098, Folio 8, Page 9
1881 Census: James (born in Bell Quay) & Sarah Gray at10 Breckon Hill, Lumley Little, Durham with two daughters Mary & Jane and son Robert). Reference is RG11, Piece 4987, Folio 69, Page 15
1911 Census: William & Jane Smith at 11 Helen Street, Winlaton, Durham (with 6 daugthers)
1901 Census: William & Jane Smith at 2 Cromwell Place, Winlaton, Durham (with 1 daughter)
Reference is RG13, Piece 4763, Folio 80, Page 39
Hope this helps...
Betty