Hi EC
Not an immediate help, but this might be Elizabeth...
at 3 Grainger St, Bishop Auckland in 1861
Elizabeth DAVISON, Head, Widow, 72, Barnard Castle
Joseph DAVISON, Son,Unm, 37, (Looks like...) Horsebreaker, Bishop Auckland
Elizabeth GREEN, Neice, Unm, 19, General Servant, Barnard Castle
Re Hardy's - mine mostly seem to come from Northumberland, with my grandmother landing in Durham sometime in the first decades of the last century!
cheers
Paul