Over at Cryptomundo, Loren Coleman correctly identifies this mystery corpse as a grey seal.
The Beast of Exmoor is a phantom cat said to live on the fields of Exmoor near Devon. During the late 1970s and 1980s, it caused a small sensation and was blamed for numerous livestock deaths. Of course, the beach creature could not possibly have been the beast, since it had fins. Hard to kill sheep with paddles for appendages.
And in another wrinkle...someone has actually stolen the skull of Beast of the Beach. A nice souvenir, so long as you really dig dead seals.