Crab claws are usually hollow to allow for the soft tissue so I am not sure that this is what it is. Horns have two componants, an outer hollow keratin sheath and an inner bone cone. When the inner bone core is broken off the skull the inside has bony shelf like structures simillar to this specimen. So I favour a horn core and from the size a sheep or goat.
We found one too yesterday!! On the bank in Greenwich. Ours is a little bigger, very blackened but looks the same as yours inside. I think it is a goat or sheep horn. God knows how old!!??