Could this be them on the 1851, transcribed as Bitby?

Mary Bitby 35 b. Poulton, Lancashire
Margaret Bitby dau 11 b. Poulton, Lancashire
James Bitby brother 40 b. Poulton, Lancashire Basket Maker
James Bitby nephew 35 b. Poulton, Lancashire Basket Maker
HO107; Piece: 2203; Folio: 331; Page: 4 Victoria Street, Warrington
JJ