I don't think there is a connection, but I have found your family on my 1881 census CD -Address - Calder Grove, Crigglestone, Yorkshire.
John Atkin, Head, age 31, born Glossop, Derbyshire, occ. Machine Man at Paper Mill.
Martha Atkin, wife, age 25, born Ecclesfield, Yorkshire, no occ..
Frances E. Atkin, daughter, scholar, born Stannington, Yorkshire.
Sarah Ann Atkin, daughter, scholar, age 6, born Crigglestone, Yorkshire.
Adelaide Atkin, daughter, scholar, age 5, born Oughty Bridge, Yorkshire.
John E. Atkin, son, age 7 months, born Crigglestone, Yorkshire.
PRO Ref. - RG11 Piece - 4571
Folio - 65 Page - 34