Born before Barbados Independence: Is she eligible?

[CuriousCam]

Hello everyone, and thank you for reading.

I have a question that I thought I would join an immigration forum to ask instead of contacting someone from the British High Commission as I am still confused, even with all the information they provide on their website.

My mother is 53 years old and lives in Barbados, which was a British colony up until 1966.
My mother was born in 1957 to an unmarried mother and father on Barbadian soil. Her father moved to England in 1959 I believe and is now a British citizen (which I am not too sure how he aquired), when my mother was a child and basically never looked back.
My mother is now a Barbadian citizen.

With the amendments made to the British Immigration acts, that would no longer bar immigration through unwed couples, I am wondering if my mother is eligible for British Citizenship/British Overseas Citizenship.

My brother just turned 21 this year, would he also be able to apply for citizenship through her if so?

Thank you

(Edit:Date Correction)

[JAJ]

Father probably (unless there were descent links to the UK) lost British nationality when Barbados became independent, but he could have re-acquired it by registration or naturalisation.

Even if parents had been married, I cannot see any basis to claim retention of British nationality at independence and/or a claim to acquire British citizenship.

Unless there are other ties to Britain or a place which remained a colony.