Hi Case,
I believe that this is your family in 1851....this is the only Thomas that fits.
Head: BERKS, Joseph Neighbors 257722
Name Relationship Mar Age Sex Occupation Birthplace
Joseph BERKS Head M 32 M Pearl Worker Birmingham-WAR
Ann BERKS Wife M 27 F At home (Domestic) Birmingham-WAR
Elizabeth BERKS Daur - 9 F Scholar Birmingham-WAR
Thomas BERKS Son - 5 M Scholar Birmingham-WAR
Henry BERKS Son - 10m M --- Birmingham-WAR
John MILES Lodg W 38 M Labourer Northleach-GLS
William ABBOTT Lodg U 20 M Brass Worker Birmingham-WAR
Address: 7 Beak Street, Birmingham
Census Place: Birmingham Birmingham, Warwickshire
PRO Reference: HO/107/2055 Folio: 312 Page: 4 FHL Film: 0087314
Hope this helps,
Cheers,
India in California