Becoming a new dad recently, prompting me to get my family tree project going again, so I've come here begging for your kind help!

I am looking for a birth record/certificate for one of my 2x great grandfather, William Hunt, who was born in 1857/8 in Lyneham, Wiltshire. He then moved with his family between 1861 and 1871 to Paddington, London.
I have got his death certificate and all the possible census from 1861 till 1911. All of them indicated that he was born in Wiltshire. I know that his mother's name is Emma Hunt (nee Vines)(b.1838 in Dauntsey, Wilts) and his father's name is Henry Hunt (b.1837 in Lyneham, Wilts) according to his wedding certificate.
All of the William Hunts that I have found in Wiltshire doesn't match with the parents name mentioned above at all.
However the only one record that I've found (so far!)that does match is located in Islington St.Mary's, London in 1855. Am I going to assume that this is the correct one?
Any help or push in the correct direction would be greatly appreciated!!

Thank you for your time reading this