We ate that korkorec on a rust bucket of boat moored by a dock, and since condemned, and we weren't very certain about it ourselves.
The mussels we had in a seafront restaurant where they are happy to let you buy them from an itinerant seller on the prom (as are all the other prom restaurants) and the waiters will actually call him over for you. I doubt that UK restaurants, and bars that sell food, would be that willing for you to have "bring in" food. It is one aspect of the cooperative, rather than fiercely competitive, side of life that you can still find in Turkey.