1861
Mosser Mains
Mosser
Cumberland
James Atkinson head mar 48 ag lab b Cumberland Bostel(?)
Susannah wife 33 b Cumberland Stableton
Bryan son 8 Lancs L'pool
Jane daur 6 do
Ellen daur 5 Cumberland Mosser
john son 2
Elizabeth daur 7 mo do
RG9/3934/85/4
So looks like your Bryan's parents are James and Susannah. You can trace their movements via the children's birth places.

Umm Carole - that 1881 is interesting ...