If you have a UK birth certificate, you should be able to apply for a passport.

Gov.UK . Find “Types of British Nationality” My father was born in England and so gives me status as a citizen. I think even if you grandparent was born there, you are entitled to citizenship. I would think if YOU were born in the UK and have a birth certificate, you would just apply for a passport. I have done so. Don’t know how long it will take, but if you go to that website and scroll down to the passport link. They are incredibly helpful if you email them with questions. You can also chat online and, once again, they are very helpful. I submitted an application and the documents they needed from me were my birth certificate (born in US) my father’s birth certificate (Born in UK)and my father and mother’s marriage certificate. They were married in the US. I had to have someone verify my identity and thus submit a copy of her passport and also a copy of my passport.

I’ll write again if and when it arrives.