You can view the 'centre point' here: -
GBPTRY=X Basic Chart | GBP/TRY Stock - Yahoo! Finance (2.8088 at the moment that I type this).
All banks and money exchanges use this same point as a reference - however, their 'profit margin' - the 'Spread' varies from establishment to establishment.
The exchange with the smallest 'spread' (difference between buying and selling price) that I have found, is the place opposite the Dome Hotel. Their 'spread' never seems to exceed 2.5 Kurus, so if, for example the current centre point is 2.80, then their spread would be approx 2.7875 (Buy) to 2.8125 (Sell).
Creditwest on the other hand use a much larger spread, often in the region of 5 to 7 Kurus. A spread of 7 Kurus based on the above would give you a range of 2.765 (Buy) to 2.835 (Sell). Currently showing their rate as:
Creditwest Bank K
The actual rate that you will get will thus obviously depend on how you transfer your money - cash in a suitcase, or bank to bank transfer, for instance, and which establishment you use to do the currency conversion.
Be aware, that if using a bank to transfer the cash, then your UK bank may charge you £30 or more, and the TRNC bank may charge up to 3% for receiving it !!! - unless you opt to allow them to convert your money to TL at a very unfavourable rate...
So, to answer your question simply, if you were in Girne TODAY, with Pounds Sterling in your hand, you would probably get something like 2.795 TL per Pound from the place opposite the Dome.
North Cyprus Currency Exchange Rates - Monexchange is showing 2.805 at the moment, but it's not always up to date, (Last Updated :07.07.2012 09:45:17 !!) and therefore not to be relied upon...
If anyone has changed money this morning, they might have a more up-to-date figure, but of course it can change minute-by-minute, although it's likely to be only by fractions of a Kurus.