Wax Cap Fungus (Hygrocybe spadicea)
The wax cap fungi belong to a family called 'Hygrocybe'. In their early stages specimens of this family often start with this distinctive conical shape and the cap is generally shiny giving the familiar name of wax cap.
Wax caps, in general, are not common and this particular species which I found at Durlston this autumn (2011) is decidedly uncommon being found only in pastures on limestone or basalt. Pasture on limestone is exactly what you find on the Dorset coast.
I have no idea whether it is edible but as it is such an attractive toadstool I think it is better left for others to see rather than to pick it for the table, there are plenty of mushrooms in your local supermarket to eat!