So this 1881?
John Bailey, 54, Flax Sail Cloth Weaver (Manuf)
Mary Bailey, 38
Mary Elizabeth Bailey, 5
Arthur Bailey, 7
Margaret Bailey, 2
Catherine Bailey, 6mths
1891 Margaret age 14 (1877) Cumberland is in Newcastle in the The Ragged and Industrial School.
1891 they are;
John Barley, 71, born Camgisle
Mary Barley, 50, born Hull
Art Aur Barley, 18, Son, born Newcastle Upon Tyne
Mary Elizabeth Barley, 14, Daug born Whitehaven
Isabella Barley, 6, Daug born Maryport, Cumberland
1901;
Mary E WILSON, 24
Margaret A Wilson, 5
Georgina Wilson, 2
Mary NANSON, 62, Mother, born Leeds**
Mary Sinton, 18
Just posting above info so others can help.
Looks to me John Bailey and Mary never married.
Also I think he had a Wife CATHERINE nee Watson in earlier Census
1881 when John is with Mary who is born Hull, this Catherine is in Yorkshire;
Catheran*** Bailey, 55, Mar, Worstead Weaver, born Carlisle, Cumberland
Elizabeth Bailey, 17, Daug, born Carlisle
John Bailey , 14, Son, born Carlisle
1871 Thornton, Yorkshire;
John Bailey, 45, Worstead Weaver, born Carlisle
Catherine Bailey, 43
William Bailey, 14
Mary Bailey, 12
George Bailey, 9
Elizabeth Bailey, 6
John Bailey, 4
John/Catherine are easy to find 1861/1871
Just my possible scenario
