Hi Mike. If you own your apartment in Fethiye and have a TAPU, you can take that.
If not then a couple of recent utility bills for your home in UK, also you will need your passports, and a Turkish tax number. You get this from the Tax office, need copies of passports, no charge.
If you plan to send money from the UK you will need a GBP account.
To pay your bills here you will need a lira daily account and if you want to earn some interest you can open a lira time deposit account.
If you want to use internet banking you should ask them to set it up for you and you will need to register a mobile telephone number with your bank. All Turkish banks now use a "one off" texted pin number for internet banking.
We use TEB and Garanti, TEB do not charge for receiving monies into your GBP account from the UK. Garanti bank offer a higher interest rate on time deposit accounts opened online. If you pay at least 2 of your utility bills by DD you probably won't pay bank charges. Otherwise there is a twice yearly charge (about 35TL) per 6 months.
Unfortunately you will not be able to open an account from the UK, you must be here to sign the forms. It will take about half an hour (in the bank) and you do not need to deposit any money at the time of opening the accounts.
Hope that helps, no doubt others will recommend other banks, but we have found that TEB are very good with paying your utility bills etc.