OK I have the process to solve this problem, and it is expensive in terms of money and time, but it does work as I can now atest, and in my case means I can properly use an expensive UK (unlocked) phone in Turkey. I will not put you off by telling you the false starts, the number of visits to Turkcell I made, or the grief along the way, or indeed the number of people and departments, and stairs I climbed up and down at the tax office - I'm getting bad flashbacks already - but simply provide you with the necessary steps you need to take.
Step One
Go to the tax office take your passport and the UK phone you want to use in Turkey with a turkish sim (this should work for all mobile companies not just Turkcell). Go to the pay office on the ground floor, join the Q, when you get to the front of the Q point to your phone say something like 'use in Turkey please' handover the phone and passport . The man will take your details including the number of the phone itself - no not the telephone number - but the one inside the phone by the bar code under the battery. You might want to practice how to get access inside the phone to this number/bar code. Once all details are entered in the computer by our tax office operative, you will be passed over to his colleague who will take 100TL for the service and give you a printed off receipt from his trusty dot matrix printer.
Step Two
Take the receipt to your mobile company's shop - suggest one of the larger shops where someone will know what to do - again give them your passport (they will need to photocopy main page plus the current visa with date of entry) and the phone. After the photocopying of all the documents and entry of your details into the Turkcell system, you will be asked to pay 10TL. Well at least that is what Turkcell charged. I was then told it would take 2-3 days but then I should put my SIM into the phone and it will work. Well I waited the 2-3 days, done as instructed and it worked. This is a new process instigated by the government and perhaps you may not need to wait 2-3 days, but I did. All I had to do then was to add a data package (1 month 4GB in my case) to my PAYG Turkcell SIM and my Galaxy S11 runs like a dream for both voice calls and data use.
Top Tip
I think I am right in saying that you can only do this once every three years, so don't look to upgrade your phone for use in Turkey anytime before then cos it won't be accepted if you make the application before the three years is up. Might be easier next time to buy an unlocked phone in Turkey, and take that back to the UK for use with your UK SIM...
Hope this helps, I'm going to lie down now with a wet flannel on my head and try to drive out the flashbacks.