Can you give date & places of birth of her husband and sons, plus Thomas' occupation.
There's this Bate family
1861 England, Wales & Scotland Census
12, Crossley Street, Warrington, Lancashire & Cheshire
Ellen Bate Head Widow 1802 Laundress Wales
William T Bate Grandson 1859 Warrington, Lancashire
EDIT - reference number RG09 Piece number 2793 Folio 87 Page 16