If you are particularly keen to see an Adonis blue butterfly then I suggest you start by going in search of horseshoe vetch (Hippocrepis comosa), the butterfly's food plant. The Adonis is not the only species that has a passion for this flower, the chalkhill blue is another, but there is undoubtedly a very close connection between the two and you will only find the Adonis where there is a very good colony of horseshoe vetch.
Being a vetch it is, of course, a member of the pea family and as such has the classic pea shaped flower. However, in horseshoe vetch the pea flowers are arranged, unsurprisingly perhaps, in a distinctive horseshoe shape around the head of the stalk; there does not seem to be a specific number of flowers per 'horseshoe'.
Flowering from May to July horseshoe vetch can only be found on short, calcareous, turf on cliffs and downs and so is extremely common near the Dorset coast, hence the abundance of Adonis blue butterflies here too.