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You can find Common Milkwort on chalk, so I don't think the amount of calcium carbonate in the soil is a good identifying factor.
Just added the underlying Geology for information. P.calcarea's preferred habitat is calcareous grassland I think, but my ID was based not on geology, just that I feel it looks more like P.calcarea.
I might be wrong and happy to be corrected. I agree entirely Bill that the geology alone is no basis for making an iD :)
Lat/Lng: 51.723, -2.2495
OS grid ref: SO828027