Well, I found a pic online that looks to be what mine is.
DEVONSHIRE CUP CORAL Caryophyllia smithii Cup 2.5cm in diameter.
The only species likely to be found. A solitary coral living on rocks from the lower shore to 100m. The polyp is translucent, of various colours. There are spherical knobs at the ends of the tentacles. Common on the west coast. May have a pink barnacle Megatrema anglicum attached to the skeleton.
The other 4 species are rare and live in certain localities in the south west of Britain e.g. Lundy, Skomer and the Scilly Isles.