I thought the OP referred to JAMES Williams not John
The OP is looking for a James Williams born Olveston circa 1845, son of James and Mary Williams. He cannot be found with certainty after the 1861 census.
(The father James Williams of Olveston Green died 27 June 1871 and left a Will, probate granted to widow Mary, and sons Joseph and Henry. Sight of the will might be instructive - does it mention son James I wonder).
The OP has found a James Williams aged 25 at a farm house in Lydney in the 1871 census, born Almondsbury (just a couple of miles from Olveston). This James is a farmer and has a wife Catharine 25 born "Slep Suldon" and a daughter Catharine 11 months old born Lydney.
There is a birth registration and a baptism for a Catherine Maud Mabel Williams born Lydney in mid-1870, parents John Robert Williams and wife Catherine Emma, nee Poole. That family lived at the Hunt farm in the 1870-1872 period. We know that JRW is not the James for which the OP is searching because his father was Edwin, not James, per the 1869 marriage record.
Catherine Emma Poole was born at Staple Hill. It is conceivable (likely?) that in that 1871 census entry, "John" has been mistranscribed as "James" and "Staple Hill" has been mistranscribed as "Slep Suldon" by the enumerator. Everything else fits the JRW family who otherwise cannot be found in the 1871 census.
My advice to Helina is to get a copy of that 1871 will and see if it mentions son James. I don't think this 1871 census entry is him.