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Thanks for your patience and enquiry. You unfortunately will require a visa in order to enter or travel through Nigeria as a British citizen.
There really is no urgent means by which you may sort this out. You would be required to apply for a visa through the Nigerian embassy. you will therefore need to check to see whether you can apply for this visa from Istanbul and how long the application process will take.
Can I clarify anything for you? I hope I have answered your query in a way that is simple and easy to understand. If anything remains unclear, I will be more than happy to clarify it for you. In the meantime, thank you once again for using our services.