ah, here are some examples:
looks like that's what you have :>
I agree part of a crab claw, but the top,pivotable pincer; & this size & shape is just right for an Edible crab, http://en.wikipedia.org/wiki/Cancer_pagurus & http://www.nhm.ac.uk/natureplus/message/30726 .NB the lack of colour could just be through 'bleaching' after a long time on the beach. I'm not familiar with the geology but http://www.berwick-upon-tweed.ukfossils.co.uk/ suggests that the cliffs here are carboniferous about 330 Million years ago
Thanks for all the answers and links.
I am gathering then that it is a crab claw but a very old one, possibly a fossilised one.
I will keep it with my little collection of things I have found