1881 Pembroke Rd Cinderford
Thos. Williams abt 1856 Cambridge, England Head Flaxley, Gloucestershire
Elizabeth Williams abt 1860 Wales Wife Flaxley, Gloucestershire
Matilda Williams abt 1880 Cinderford, Gloucestershire, England Daughter Flaxley, Gloucestershire

Name: Matilda Williams
Year of Registration: 1879
Quarter of Registration: Jul-Aug-Sep
District: Westbury On Severn
County: Gloucestershire
Volume: 6a
Page: 251

Cambridge ?
Thats either Cambridge nr Dursley Glos, or perhaps its a mis heard Nailbridge.

If Nailbridge is correct then it tends to lead to :-

1861
Hannah Howells abt 1822 East Dean, Gloucestershire, England Head Abinghall, Gloucestershire
Anne Howells abt 1844 East Dean, Gloucestershire, England Daughter Abinghall, Gloucestershire
Charlotte Baldwin abt 1848 East Dean, Gloucestershire, England Daughter Abinghall, Gloucestershire
William Baldwin abt 1846 East Dean, Gloucestershire, England Son Abinghall, Gloucestershire
Thomas Williams abt 1856 East Dean, Gloucestershire, England Boarder Abinghall, Gloucestershire

maybe :-

Name: Thomas Williams
Year of Registration: 1855
Quarter of Registration: Jan-Feb-Mar
District: Westbury On Severn
County: Gloucestershire
Volume: 6a
Page: 193

or on Ruardean Hill in 1871

1871
William Williams abt 1806 Repton, Herefordshire, England Head East Dean, Gloucestershire
Esther Williams abt 1815 Walford, Herefordshire, England Wife East Dean, Gloucestershire
Edwin Williams abt 1850 East Dean, Gloucestershire, England Son East Dean, Gloucestershire
James Williams abt 1858 East Dean, Gloucestershire, England Son East Dean, Gloucestershire
Lydia Williams abt 1854 East Dean, Gloucestershire, England Daughter East Dean, Gloucestershire
Tom Williams abt 1856 East Dean, Gloucestershire, England Son East Dean, Gloucestershire

however this Tom shows as
1861
Thomas Williams abt 1846 Ruardean Hill, Gloucestershire, England Son East Dean, Gloucestershire