Pets from Turkey are OK, providing the following is adhered to.
From the Defra website:
What you need to do if you are entering the UK from unlisted non-EU countries
Preparing your dog, cat or ferret
Step 1 - Have your pet microchipped - Before any of the other procedures for pet travel are carried out, your pet must be fitted with a microchip so it can be properly identified.
Step 2 - Have your pet vaccinated - After the microchip has been fitted your pet must be vaccinated against rabies. There is no exemption to this requirement, even if your pet has a current rabies vaccination. Rabies boosters must be kept up to date.
Step 3 - Arrange a blood test - After your pet has been vaccinated, it must be blood tested to make sure the vaccine has given it a satisfactory level of protection against rabies. The blood sample must be taken at least 30 days after vaccination. The length of the waiting period before entry to the UK is three calendar months from the date your vet took the blood sample which led to a satisfactory test result. The 3 month waiting period will not apply if your pet was vaccinated and blood tested in the EU and issued with an EU pet passport before it went to an unlisted unlisted country.
Step 4 - Get pet travel documentation -You will need to obtain an official third country veterinary.
Step 5 - Tapeworm treatment - We expect the European Commission to shortly come forward with proposals to allows the UK to still require pets to be treated against tapeworms. There will be no mandatory requirement for tick treatment.
Step 6 - Arrange for your animal to travel with an approved transport company on an authorised route - Your pet must enter the UK with an approved transport company on an authorised route.