Hi
The 1851 census of Tivetshall has the following;
Thomas Scoulding 37 Ag Lab Tivetshall
Elizabeth ,, 32 Aslacton
William Woodcraft 12 Tivetshall
James Scoulding 10 ,,
George ,, 8 ,,
Mary Ann ,, 6 ,,
Robert ,, 4 ,,
Susanna ,, 1 ,,
I suggest then that you look for the marriage of Thomas Scoulding and Elizabeth Woodcraft in Aslacton or Tivetshall in 1839-41. I may be wrong but it looks that your William was born outside wedlock but took the family name at some stage. He was put down as son in the census.
Best wishes
Teddy