From The West Wiltshire District Guide 1978:
Coulston (spelt Covelestone in 1086) has a population of only 118, yet it was divided into two portions until a very few years ago.
West Coulston was a tithing of the neighbouring parish of Edington, and East Coulston was a separate parish with its own church. The parish boundary ran throughBaynton House, south-west of the church.
The dedication of the church was St. Andrew, but for the last 200 years it has been known as the Church of St. Thomas a’ Becket.
Becketts were considerable landowners in the area for many years after the Reformation, and this may account for the change of title. Houses in Edington and West Lavington still retain their name.