William gives p.o.b. as Norwich Norfolk on 1851 census
1841 census only gives "Yes or No" in answer to state whether born in county (not town/village etc) they were living in
As William was living in St Martin at Oak it does not necessarily mean he was born there.
1841 census (ages of adults over 15 rounded down to the nearest 5 years)
Oak St
St Martin at Oak Norfolk
William Slater 35 worsted weaver
Elizabeth 11
William 9
Robert 7
Esther 3
all born in county
HO107 789 9 48
as Mary Ann is not on census maybe she had died

It seems William possibly remarried
there is this marriage reg FreeBMD
Dec qtr 1842
Purchase of Marriage cert would give father's name & occupation
1851
Angel Yard Oak St Norwich Norfolk
William Slater Head Married 46 silk weaver
Susannah wife Married 38 Silk Weaver
Esther daughter 13 Silk Winder
Susannah daughter 2
all b Norwich Norfolk
HO107 1812 167 43
There is this baptism on family search - which is a possibility for your William
William Slater
baptised 24 Jun 1804 St Margarets Norwich Norfolk
Parents William Slater & Esther Betts
Suz