Quite apart from the citizenship by descent aspect, it is quite possible that your mother was not a British citizen at the time of your birth, but a British Overseas Citizen (BOC), a status that cannot be inherited unless you are stateless.
Before 1983, there were two separate statuses. Your mother was a CUKC (Citizen of the United Kingdom and Colonies) by descent from her father, who was born on a British colony. However, she did not have the Right of Abode (RoA), a status which she would get only if she had either an ancestral (from either parent) or residential link to the UK itself (i.e. not to a colony).
Therefore, if neither she nor her parents resided or had some connection (birth, registration or naturalisation) in the UK, she would have been a CUKC without RoA.
In 1983, the law changed, so that CUKCs with RoA became British citizens, while CUKCs without RoA became
British Overseas Citizens, who did not have the right to reside in the UK, even though they had British passports.
It may be worth checking your mother's old passports to see if she was a British Citizen or a British Overseas Citizen. I think, based on the information that you have provided so far, that she was a BOC at the time of your birth and therefore that you would not be able to inherit that status anyway.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.
