it shouldn't make a difference, but to avoid confusion at the airport (and genreally anywhere in Turkey lol) go with the easiest and most obvious solution - so if you passport is UK, then pay in sterling!
As for what money to bring - dont bring much in euro/sterling. just enough to get by - then take the rest out at an atm - this is the easiest way I find. Otherwise you end up either bringing a lot of lira in cash with you - and carrying a lot of cash in any currency is never a good idea. Or you bring sterling/euro and then end up chaning it there anyway!
And as for not charging commission over there like all the signs say - twaddle! unless you exchange in a bank where you have an account you will pay a small commission -
(between 5-10 lira per 100 sterling/euro).
my advice is to bring yor atm card, take out a decent amount to last you a couple of days, take it out in local currency. when you spend it go back to atm - much better than carrying wads of cash in any currency around, and comission wise it's about the same price anyway.