Was that the 1871 census for the Williams Family in West Derby ?

1881 at 122 Killshaw St. Everton Liverpool.

James Williams 49 Walford Hereford Cabman
Sarah 32 Prescot Lancs
Susannah 18 Colford Gloucester
Christopher 11
Sarah Ann 10
Elizabeth 8
Emmeline 5
Gertrude Blanch 3
Isabella 1
Louisa J Williams Niece 21 West Derby

There's still the connection to Coleford but James appears to have shifted.

Len Faragher