without starting a search the fact that you are having difficulty in this time frame suggests a Non conformist tradition - does that fit with anything you already know ?
1851 Old Croft
Thomas Williams abt 1817 Lisney, Gloucestershire, England Head West Dean, Gloucestershire
Ether Williams abt 1829 Lisney, Gloucestershire, England Wife West Dean, Gloucestershire
Lennerd Williams abt 1845 West Dean, Gloucestershire, England Son West Dean, Gloucestershire
Richard Williams abt 1847 West Dean, Gloucestershire, England Son West Dean, Gloucestershire
Charlott Williams abt 1850 West Dean, Gloucestershire, England Daughter West Dean, Gloucestershire
Henry James abt 1807 West Dean, Gloucestershire, England Lodger West Dean, Gloucestershire
1861
Thomas Williams abt 1816 Lydney, Gloucestershire, England Head Lydney, Gloucestershire
Ester Williams abt 1821 Lydney, Gloucestershire, England Wife Lydney, Gloucestershire
Leonard Williams abt 1845 Lydney, Gloucestershire, England Son Lydney, Gloucestershire
Richard Williams abt 1847 West Dean, Gloucestershire, England Son Lydney, Gloucestershire
William Williams abt 1856 West Dean, Gloucestershire, England Son Lydney, Gloucestershire
Tom Williams abt 1858 West Dean, Gloucestershire, England Son Lydney, Gloucestershire
John Williams abt 1860 Lydney, Gloucestershire, England Son Lydney, Gloucestershire
--
Ἀριστοτέλης A Gloster & Hereford Boy in the Forest of Dean ><((((*>