If they do insist on photographic ID, then sue them for defamation of character. If they're accusing you of being a terrorist with no evidence whatsoever then they deserve to be taken to the cleaners for every penny they've got.
Just to stir up a debate.....Northern Ireland is NOT part of the UK but IS part of Great Britain. UK is the Scotland/England/Wales mainland, GB includes Northern Ireland, British Isles include the Irish Republic. A passport is not required for travel within GB.