I have identified these both as the Common Milkwort, Polygala vulgaris. The reason was based on the long slender leaves on the stem where as the Chalk Milkwort, Polygala calcarea, usually has blunter leaves.

You first suspect you might have a plant of Polygala calcarea when you see several tight bunches of flowers arranged like the outer parts of spokes of a wheel. Next you have to get down close to the plant to see how it is where it comes out of the ground. This may be quite difficult because it means separating it from the rest of the vegetation; this is a plant of good calcareous grassland which has lots of species all tangled up together. You know you've got the right thing when you find that the very lowest aerial part of the plant is a slender unbranched leafless stem which may be as much as 50 mm long. Above this there are several very closely spaced leaves, not quite in a rosette, and the branching points where those radiating flowering stems start. The leaves on those stems do not get bigger as you get nearer the flowers, as they do in P. vulgaris.

Chalk Milkwort (BioImages)
http://www.bioimages.org.uk/html/P1/P18511.php

Wild Flowers Forum Discussion
http://www.wildaboutbritain.co.uk/forums/wildflowers-plants-tree-forums/11080-flower.html?posted=1#post119753