Hi Vanessa
Could you post 1851 details for William Palmer - where was he living? parents or siblings with him? I'll try looking for him in 1841. Ann too if you know maiden name.
I'll post the family I found in Barrow as it is the best match I can find, in case they do turn out to be yours. Best of luck with your continued search, let us know how you get on.

Jan
1871
Barrow, Boddington
Joseph Freeman Head Mar 49 Labourer Boddington
Sarah Freeman Wife Mar Wife ? Rostbury (the ? is the enumerators not mine, no county given)
Albert Freeman Son 12 Boddington
Martha Do Daur 10 Boddington
Henry Do Son 7 Boddington
Ann Do Daur 3 Boddington
RG10/2676 ED10 Folio114 Pg6
1881
Barrow Boddington
Joseph Freeman Head Mar 59 Farm labourer Gloucs Barrow
Sarah Freeman Wife Mar 57 Household Work Gloucs Pristbury
Albert Do Son Unm 22 Farm Labourer Barrow
Martha Do Daur Unm 19 Plain server Barrow
Henry Do Son Unm 17 Farm Labourer Barrow
Annie Do Daur 13 Scholar Barrow
RG11/2579 ED24 Folio130 Pg4
1861
Boddington Manor, Boddington
Joseph Freeman Head Mar 39 Ag Lab Boddington
Sarah Freeman Wife Mar 36 Gloshire (sic) Prestbury
Alice Do Daur 6 Boddington
Hannah Do 5 Boddington
Albert Do Son 2 Boddington
RG9/1804 ED96 Folio1 Pg4
and for good measure in 1841
Boddington
Henry Freeman 45 Ag Lab Yes
Edith Freeman 45 Yes
Joseph Freeman 15 Yes
HO107-0367 ED10 Folio8 Pg11
Shame if they're nothing to do with you
