Common names include Sea Fig, Western Iceplant, Coastal Iceplant, Baby Sun-Rose, Angled Pigface, I can't understand the 'Pigface' name.

Carpobrotus edulis is a southern African plant. Introduced to Europe, the plant can be found entirely naturalised in some coastal habitats, particularly sea cliffs and sand-dunes in the south west of the UK. The plant tends be quite invasive, spreading and forming continuous mats over large areas. It does look stunning, but there may some problems with it. First of all it is not indigenous, and is colonising this area to the detriment of other natives such as thrift. Also it is a succulent and holds on to water, becoming heavy in wet weather. Whole mats of it can become dislocated from the cliffs causing rock falls.

I'm not sure what the policy is in Budleigh. Maybe in certain areas the plants should be eradicated to allow indigenous species to thrive in order to prevent more coastal erosion.