Three-veined sandwort (Moehringia trinervia) has a tiny star shaped flower despite the plant itself being quite sturdy with pointed leaves in opposite pairs. Running the length of the leaves are three distinctive veins (tri-nervia) which give the plant its name; in some books it is actually called three-nerved sandwort. Apart from the leaves its other distinctive feature is its long pointed sepals that extend beyond the petals.
Easily dismissed as lesser stitchwort or, perhaps, a mouse-ear, three-veined sandwort occurs in woodlands on rich soils flowering from May until July. You might expect to see it on sandy soils (sandwort) but it is most often found on bare, muddy paths in broad-leaf woodland.
This is not a common plant in Dorset although it can be quite well established where it does occur.