I can't see William in the 1851 either- although we know he's not with his family:
1851 England Census
Name: Elizabeth Cookson
Age: 53
Estimated Birth Year: abt 1798
Relation: Head
Gender: Female
Where born: Walworth, Surrey, England
Civil Parish: Ilminster
Town: Ilminster
County/Island: Somerset
Country: England
Condition as to marriage: Widow
Registration district: Chard
Sub registration district: Ilminster
ED, institution, or vessel: 11d
Household schedule number: 118
Household Members: Name Age
Elizabeth Cookson 53
Laura Cookson 26
Lilia Cookson 24
Emma Cookson 19
Adela Cookson 12
Osmond Cookson 10
Caroline Willham 22 (servant)
Mary Bailey 22 (servant)
Maria Scott 11 (Visitor)