No Visa's required for Turkey or Israel with British Passport. A visa is require for Egypt but they normally issue a 'block' visa to cruise ships & the cruise lines deliver them to your cabin prior to arrival. Americans also need this visa so it would be a fair assumption this will be handled by 'O'. Why not email their clueless department.
If you are flying into Turkey you NEED a VISA
You can get it before you go or at the airport for CASH.
If you are flying out of Turkey you NEED a VISA
If you are just stopping in Turkey on a cruise you DO NOT need a visa