As indicated in an earlier reponse this family is not from the Forest of Dean to which this site is dedicated. That said we know from the 1851 Census that William Williams was aged 45 and gave his birth place as Sevenhampton.
Search the IGI at http://www.familysearch.org/Eng/Search/frameset_search.asp
and you will find this entry:
17 January 1805 William WILLIAMS baptised at Sevenhampton. Parents: Samuel WILLIAMS and Sarah.
A further search gives this as a possible marriage for Samuel:
18 November 1799 Samuel WILLIAMS married Sarah HAWKES at Whittington.

This could be Samuel in 1851 Census:

1969 0315 080 Whittington TURNER Jasper HD M 29 Agricultural Labourer GLS Whittington
1969 0315 080 Whittington TURNER Elizabeth WI M 30 - GLS Foxcote
1969 0315 080 Whittington TURNER Solomon SO - 9 Farmers Boy GLS Sevenhampton
1969 0315 080 Whittington TURNER William SO - 7 Scholar GLS Charlton Abbots
1969 0315 080 Whittington TURNER Roseanna DA - 5 Scholar GLS Whittington
1969 0315 080 Whittington TURNER Isabella DA - 3 - GLS Whittington
1969 0315 080 Whittington TURNER Elizabeth DA - 8M - GLS Whittington
1969 0315 080 Whittington WILLIAMS Samuel FL W 76 Pauper Late Farm Labourer GLS Guiting Power

This entry from GFHS Burial Index:
Date: 23 JUL 1843
First Name: SARAH
Surname: WILLIAMS
Age: 65
Burial Register: WHITTINGTON 1813-1851
Place of Abode: SEVENHAMPTON

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Mike