Al
I don't know for sure what N&P policy is, but Nationwide used to pay (almost) the Interbank Exchange Rate. This is the rate at which banks trade with each other and is based on deals worth over $1 million. This is the figure you see when you look at most foreign exchange data in the financial press or online (but I'm not sure about CBF's link since it seems Coinmill uses a different method but arrives at more-or-less the same result). I have checked this when withdrawing cash and found the difference between published FX rates and what I am charged by my bank to be insignificant - about one penny per £100. So if you see the rate published at £1 = 2.562 TL then that is the rate you get (bearing in mind that the exchange rate varies over the day so it depends on exactly when the Turkish bank whose ATM you used charges your UK bank - I guess at close of the Turkish banking day, or possibly on a daily mean average rate). It is, I believe, the best rate you can get. [I am assuming that N&P is the same].
P.S. Looking into this a little more I find that the rate is actually based on the Visa/Mastercard Wholesale Rate which is calculated the day before and applies to all participating banks on the next day. However, since this rate mirrors market rates - which is what the Interbank Rate measures -it makes no significant difference to what I said above but probably accounts for the very slight variation I noticed. It also confirms that this is the rate applied by N&P.