I am afraid I am not sure what the answer to your question is, but thought with such a complex question it might be a good idea to consult the forgein ministry of turkey.

According to their site (http://www.mfa.gov.tr/visa-information- ... ers.en.mfa):

"United Kingdom: Ordinary and official passport holders are required to have visa to enter Turkey. Ordinary passport holders can obtain three month-multiple entry visas at the Turkish border Gates. “British National Overseas ( BNO )” or “British Protected Persons ( BPP )” passport holders are NOT issued visas on the Turkish border Gates They must apply to the Turkish representations abroad in order to get visa ( Hong Kong citizens holding BNO passport can obtain visa on the border gates )."

It appears you need a apply for a multiple-entry visa (Muteaddit giris). A multiple-entry visa, on the other hand, permits multiple entries into the country within the span of its validity without incurring any additional cost. If you plan to enter and leave Turkey 4-5 times in a span of three months, for instance, it is worthwhile going for a "Muteaddit giris"

Hopefully that helps!