Carrot Broomrape (Orobanche maritima)
Broomrape flowers are parasitic on various plants, this one on Wild Carrot, of course, but there are also Broomrapes that are parasitic on Yarrow, Ivy, Knapweed, Bedstraw, Thyme, Oxtongue and Thistle.
Because they are parasitic they have no chlorophyll as they do not need to use the sun to create growth, they get their nutrients from the host plant. As they have no chlorophyll they are not green like most other flowers and it easy to pass them by thinking that you are looking at a dead flower head rather than a real live flower.
All members of the Broomrape family are similar to look at with the differences between the species being quite limited. The Carrot Broomrape is quite uncommon, found only on the south coast of England, and the sea cliffs of Dorset is a good place to look for it among the Wild Carrot flowers.