Me again

The 1851 Census shows...
1851 Census England Warwickshire Thurlaston
HO107/2070/236/5
GARNER
William Head Marr 45 Carpenter Warwickshire Willenhall
Elizabeth Wife Marr 43 Warwickshire Foleshill
James Son Unmarr 11 Warwickshire Thurlaston
John Son Unmarr 8 Warwickshire Thurlaston
Hannah Dau Unmarr 5 Warwickshire Thurlaston
Caroline COCKERILL Dau Unmarr 4 Warwickshire Thurlaston
James COCKERILL Son Unmarr 6 Warwickshire Thurlaston
William COCKERILL Son Unmarr 2 Warwickshire Thurlaston
Thomas HILL Lodger Marr 51 Drawer Warwickshire Thurlaston Blind
Hannah HILL Lodger Marr 52 Warwickshire Cubbington
So it appears that William remarried after Rebecca's death.
Marriage Register
Parish Church Leamington Priors
Warwickshire
6th Jan 1851
William GARNER of full age Widower Carpenter of " The Green Man" Grove Place Father = Thomas GARNER Gardener
Elizabeth COCKERILL of full age Widow of Grove Place Father = William BALL Labourer
The groom signed and the bride made her mark
Witnesses were Gilbert?? COCKERILL who made his mark and

COCKERILL who signed ( very badly )
ADDED.. just found... marriage between Basil COCKERILL and Elizabeth BALL 9th Sept 1828 Coventry Warwickshire. Burial 11th Jan 1849 for Basil