You say that you can't find William in the 1851/1861 Census does that mean you've found him in the other Census? As you can see the Census below seem to tie into 'your' Rachel but the William listed here is from Wales. Do any of their children tie in with any information you already have?
1841 Wales Census (a possible)
James King abt 1836 Monmouthshire, Wales St Brides Netherwent Monmouthshire
John King abt 1796 Monmouthshire, Wales St Brides Netherwent Monmouthshire
Rachel King abt 1825 Monmouthshire, Wales St Brides Netherwent Monmouthshire
Sarah King abt 1796 Monmouthshire, Wales St Brides Netherwent Monmouthshire
William King abt 1830 Monmouthshire, Wales St Brides Netherwent Monmouthshire
1851 Wales Census (a possible)
Sarah King abt 1793 Gloucestershire, England Head St Bride Monmouthshire
William King abt 1827 St Brides, Monmouthshire, Wales Son St Bride Monmouthshire
James King abt 1836 St Brides, Monmouthshire, Wales Son St Bride Monmouthshire
1861 Wales Census (as transcribed)!
John Hing abt 1853 St Brides, Monmouthshire, Wales Son Undy Monmouthshire
Rachel Hing abt 1833 St Breviale, Gloucestershire, England Wife Undy Monmouthshire
Sarah A Hing abt 1857 St Brides, Monmouthshire, Wales Daughter Undy Monmouthshire
Thomas Hing abt 1855 St Brides, Monmouthshire, Wales Son Undy Monmouthshire
William Hing abt 1828 St Brides, Monmouthshire, Wales Head Undy Monmouthshire
William Hing abt 1860 St Brides, Monmouthshire, Wales Son Undy Monmouthshire
1871 England Census
Albert King abt 1866 St Bride, Monmouthshire, Wales Son Aylburton Gloucestershire
George King abt 1869 St Bride, Monmouthshire, Wales Son Aylburton Gloucestershire
James King abt 1864 St Bride, Monmouthshire, Wales Son Aylburton Gloucestershire
John King abt 1852 St Bride, Monmouthshire, Wales Son Aylburton Gloucestershire
Rachael King abt 1833 St Briavels, Gloucestershire, England Wife Aylburton Gloucestershire
Sarah A King abt 1856 St Bride, Monmouthshire, Wales Daughter Aylburton Gloucestershire
Thomas King abt 1855 St Bride, Monmouthshire, Wales Son Aylburton Gloucestershire
William King abt 1823 St Bride, Monmouthshire, Wales Head Aylburton Gloucestershire
William King abt 1868 St Bride, Monmouthshire, Wales Son Aylburton
1881 England Census
Albert King abt 1866 Magor, Monmouth, Wales Son St Briavels Gloucestershire
George King abt 1869 Magor, Monmouth, Wales Son St Briavels Gloucestershire
James King abt 1862 Magor, Monmouth, Wales Son St Briavels Gloucestershire
Rachel King abt 1836 St Briavels, Gloucestershire, England Wife St Briavels Gloucestershire
William King abt 1821 Magor, Monmouth, Wales Head St Briavels Gloucestershire
William King abt 1860 Magor, Monmouth, Wales Son St Briavels Gloucestershire
1891 England Census
Albert King abt 1867 St Bride's, Monmouthshire, Wales Son Tidenham Gloucestershire
Rachel King abt 1826 St Briavels, Gloucestershire, England Wife Tidenham Gloucestershire
William King abt 1824 St Bride's, Monmouthshire, Wales Head Tidenham Gloucestershire
Sarah Kingdon abt 1876 Bristol Servant Tidenham Gloucestershire
1901 England Census
Pricella King abt 1888 Tidenham, Gloucestershire, England Granddaughter Tidenham Gloucestershire
Rachel King abt 1825 St Briavels, Gloucestershire, England Wife Tidenham Gloucestershire
William King abt 1822 St Bride's, Monmouthshire, Wales Head Tidenham Gloucestershire