I agree with Eric, speak to Defra.
We brought our old mut over from the uk nearly 3 years ago. As long as your travelling with your pet its very easy, just get the appropriate form from Defra which needs to be filled out and sent back to them for signatures..they then send it back to you. You need upto date vacinations including rabies, and a signed certifition from your UK vet within 96 hrs of travelling. Lastly you need to ensure that you have the appropriate travelling box for your pet, advised by defra and ordered on the internet.
Certainly at the time we brought our dog over, a passport for the dog wasnt needed as Turkey is not EU.
We flew out with Turkish airways at the time, changing via Istanbul and into Izmir. They were fantastic.
Harvey came out on the conveyer belt at Izmir airport, unscathed, if a bit confuse and is now having a great life out here with us.