Ploughman's Spikenard (Inula conyza)
It grows on calcareous soils on wasteland, grassland and scrub and so will be found on the Purbeck Ridge and along the cliffs where the earth is, perhaps, a bit bare.
It has a strange name and I have no idea where it comes from. Agreed it is a bit prickly, or spiky, and it is out in the late summer and early autumn when traditionally the fields would have been ploughed after the harvest so perhaps Ploughman's Spikenard is something to do with the spiky plant that ploughmen tread on?
It is a member of the daisy family and the nondescript flower heads turn into clusters of seeds heads, much like a Groundsel.