The U.K. has a consulate in Istanbul, Turkey. (All the embassies are in Ankara). Below are the details.
British Consulate-General, Istanbul Meşrutiyet Cad No.34 Tepebaşı Beyoğlu 80050 Istanbul
Dave's Travel Pages has a number of affiliate links placed within the travel blog. If you decide to buy items through these links, you will be helping Dave to fund this site and perhaps the next adventure. More importantly, it doesn't cost you anything extra. Win win - we like that!