Ah, so this could be a problem. The big question then, is where your mother was living when these colonies became independent - 1964 for Zambia and Malawi, 1965 for Zimbabwe. (If she is from Zimbabwe the situation is more complicated than Zambia and Malawi, or at least that is my understanding.)
Why this matter is, if she was living in the colony when it became officially independent, she should have lost her UK subject status and you are not a British citizen. However, if she had left the colony before independence, she likely retained the status. The question would then become what that entitles you to now.
Make sense?