The vegetation in wet areas of heath is, naturally, very diffferent to that of dry heath. Whilst some plants occur in both, in general each species has its preference for areas of wet mire and bog or dry, sandy soil. It should not come as a surprise, then, that marsh pennywort (Hydrocotyle vulgaris) favours damp bog and fen. It also has a preference for acid conditions so the wet areas on the Dorset heaths is a place you are likely to find it.
If you are looking for a flower to identify it by you are most likely going to struggle because the flowers are very small, green in colour and are formed in a tight ball so although flowers are present from June in to August they are not readily visible! Fortunately the leaves are quite distinctive being disc-like forming a very shallow cone. The leaves recall water-lily in some ways as they tend to float on standing water if present.Not over common in my experience but where it does occur
Read more: Marsh Pennywort: the answer lies in the leaves