I couldn't find any Hannah Beswicks on the 1861 that matched the information you provided. I did find a Hannah Taylor, 30, born in Rostherne, Cheshire as follows:
1861 census - Rostherne, Cheshire
Hannah Massey, head, unmarried, 60, shopkeeper ??, Rostherne, Cheshire
Samuel Taylor, nephew, married, 30, agr lab, Rostherne, Cheshire
Hannah Taylor, neice, married, 30, Rostherne, Cheshire
James Stanley, visitor, married, 24, taylor journeyman, Manchester, Lancashire
Mary Ann Stanley, visitor, married, 21, Manchester, Lancashire
Charles E. Stanley, visitor, single, 3, Manchester, Lancashire
Piece 2594, Folio 86, Page 7
This is the only Hannah Taylor born in Cheshire about 1831 with a husband named Joseph that I could find:
1861 census - Storeton, Cheshire
Joseph Taylor, head, 30, agric lab, Bebington, Cheshire
Hannah Taylor, wife, 29, Bickerton, Cheshire
Mary Taylor, daughter, 4, Bickerton, Cheshire
Piece 2637, Folio 7, Page 7
There is another possibility. On the 1871 census there is a Joseph and Hannah Taylor in St. John, Cheshire. Joseph is a cooper and their oldest two children are Martha (14) and Arthur (11). I found an entry in 1861 for a Joseph and Harriet Taylor that matches much of the information from the 1871 census.
1861 census - Chester St John The Baptist, Cheshire
Joseph Taylor, head, 34, cooper, Cheshire
Harriet Taylor, wife, 30, Cheshire
Harriet Taylor, daughter, 10, Cheshire
Martha Ann Taylor, daughter, 4, Cheshire
Henry Arthur Taylor, son, 1, Cheshire
Piece 2625, Folio 14, Page 21
There are two births for Harriet Taylors in Great Boughton one registered in the third quarter of 1850 and another in fourth quarter of 1851. There is also a death registration in Great Boughton for a Hannah Taylor in the second quarter of 1863. There were no deaths for Harriet Taylors in Great Boughton. It seems possible that the 1861 Harriet (mother) could be the 1871 Hannah and the 1861 Harriet (daughter) could be the one who died in 1863.
Jacquie
