One of several sarsens in front of Christ Church, East Kennet

Where there are stones there often seems to be a nearby spring or well and/or a river. In the Avebury/Silbury area there are eight churches close to the course of the Winterbourne and Kennet, several with what appear to be un-worked stones in their foundations. The same also at nearby Alton Priors, Clyffe Pypard, Pewsey and, in Essex, at Alphamstone and The Church of St Mary with St Leonard, Broomfield, Chelmsford. See -
At East Kennet, "There was a church on the same site as the present one in the 12th century... local poverty and negligence on the part of the owner... resulted in reports in the 16th and 17th centuries of the decay of the church fabric, and by the 19th century the church had become dilapidated." (from the church information sheet).
It seems the old church was completely demolished in the 19th century and then a new one built in the Early English style. That might account for there being nothing of megalithic interest in the church foundations. However, the site does have a 'pre-Christian feel' to it. The church is built on a slight mound. There's a yew tree in its churchyard (about as old as the one at Alton Barns) and a pond on the outside of the churchyard wall with one large sarsen (maybe two sarsens as there's something completely covered with ivy) at the pond's edge. There's also another large sarsen in a nearby garden and a heap of broken sarsens by the northern wall of the churchyard. The original church may have been built within a circle not on it.