Hello and welcome to RootsChat !
The William Place born abt 1827 Lakenheath seems to be on the 1851 census with wife Betsey and is still in Lakenheath :
HO107; Piece: 1830; Folio: 144; Page: 40.
Looking at the Tostock Place family they have :
William Rushbrooke Place 19 Apr 1929 Tostock St Andrew , parents William , shop porter,
and Sarah. Their residence is given as Bury St Edmunds.
They also have Rose Anna 1827 and Susan 1823.
There is a burial for William Place , born about 1802 , in Bury St Edmunds in 1830. I would suggest this is William the father.
there is a likely baptism for William senior in Tostock 26 May 1801 , parents Thomas and Rose - they were formerly of Rushbrooke , which would account for the son's name.
I think your William is on the 1841 census as a male servant in the household of John Watson , grocer , in Bury St Edmunds .
Hope this helps !