Unfortunately you cannot acquire
British Citizenship, if you are unable to show both your father and mother were married, at the time of your birth or after.
I feel sorry that this may affect your aspiration, but it is how the rules are. You may succeed on the basis of age discrimination to fight it, because children born before 1 July 2006, who are under 18 can register as British if there parents were unmarried at the time of their birth, although this is at the Secretary of States discretion under section 3(1) but this is inapplicable to adult aged potential beneficiary. It seem totally flawed to me, and you could certainly fight it if you so wish. Provided you are prepared to foot the cost.