See the Baptism Index at http://www.cfhs.org.uk/cgi-bin/baptismindex.cgi
It shows Edward and Sarah baptising William T Marriot in Royston in 1825. As Royston was mainly in Hertfordshire you'll find the baptism of William Thomas Marriot son of Edward and Sarah at Royston Herts on 13 Oct 1825 on the IGI at www.familysearch.org
. . But the marriage certificate as quoted by Judith names his father as George. So is Royston parish register in error when it names his father as Edward? Finding the baptism of William's brother Alexander might help solve the anomaly. Alexander was buried at Cambridge St Paul on 1 Mar 1906 age 83.
Other than the marriage certificate is there any other evidence that he was the son of George, and what's to prove that George was from Surrey? I question your death year of 1873 for George. He was described as deceased on William's marriage in 1846 and in William's obituary it states that both his parents had died when he was but a youth.