It is interesting that Stephen knew his fathers name. I dont think that was very common for illegitimate children.
Here is a possible father, in the approximate place and free at the right time.
This George STRUDWICK is a carpenter / builder through various records and may have had something to do with his son Stephen going into a similar trade. Just speculation.
George STRUDWICK bapt 26 Dec 1819 Holy Trinity Guildford
to parents William (occupation carpenter) and Jane STRUDWICK
1841 census
https://www.familysearch.org/ark:/61903/1:1:MQKZ-73BHis father is a builder, and George is an apprentice
In 1851 Guildford
George Strudwick 31 Carpenter, born Guildford
Mary Ann Strudwick, wife, 25, born Alford
Jane Strudwick, 5 months
His wife was Mary Ann HEATHER.
George and Mary Ann married 29 Nov 1849 in St Mary Islington.
The Strudwick family stay in Guildford through the census records.