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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