Familysearch has the marriage (transcribed as Hardin) 11/9/1859, Hale, Surrey. Grooms father also William Silas Harding. Grooms age 21 (1838)
Also on Familysearch is the baptism of William Silas. 25/3/1838, Elstead, Sry. Mother, Hannah Harding. With just the mothers name being mentioned it looks like he was illegitimate.
It must be the 1851 census you're talking about. He's with a John & Ann Jeffery in Frensham.
There are two deaths recorded on FreeBMD for Hannah Harding in Hambledon RD (of which Elstead is a part of) Q2 1839 & Q3 1839. One of these might be her & the reason why William is with an uncle,
PS. He's also with John & Ann Jeffery in 1841 at Frensham.
Jane