Depending on common English names to identify plants can lead to mistakes but in the case of heath bedstraw (Galium saxatile) you are on fairly safe ground (as long as the ground is acidic!). Heath bedstraw is by far the most common member of the bedstraw family to be found on heaths and acid grasslands. In fact, in Dorset, you can be pretty sure that it is the only one.
Heath bedstraw in a low growing, somewhat sprawling plant that can form quite large mats of vegetation. The creamy white flowers appear from May through until August and, if you get down on your hands and knees and have a sniff you will find them fragrant. I would say that this plant is most common in dry, grassy areas but it can occur amongst heather and can even colonise rocky areas.