The excellent BGS webpage Geology of Britain has links to borehole reports as well as to the underlying geology.
Or in 3D - http://mapapps.bgs.ac.uk/geologyofbritain3d/index.html
Click to enlarge.
If you try the links on the new boreholes to the north of Winterbourne Stoke (on the BGS website) it shows they are from the Stage 2 of the A303 investigation and the results aren't available (yet?) and some are confidential...
But I think we can see the routes they are thinking of.
The bright green splodges are the phosphatic chalk deposits.