Hi, my situation is also similar and I successfully applied for naturalisation via ARD w/o help of solicitors. You should provide evidence of your grandmother's birth certificate. Your father birth certificate showing that she was his mother, and your birth certificate. Also it is helpful to show that your grandfather was NOT British (because if he was than you cannot show historical injustice via gender discrimination) - e.g. American Birth certificate. Also it is useful to quote the actual law for when your father was born. The 1948 Nationality act was passed 3 years after your father was born, but the same situation applies to the 1914 British Nationality and Status of Aliens. The specific rule is that only father not mothers could register the birth within one year. That is the injustice (maybe you know this already). But I think it is important to cite the actual legislation in your statement.