You mentioned that your father's family is resident in the UK. Is your father British? You could claim citizenship from him.
What was the last British passport held by your mother and when and where was it issued?
As Wanderer mentioned, your mother was likely a CUKC (Citizen of the United Kingdom and Colonies). After 1983, with the passage of the British Nationality Act 1981, any CUKC without a direct link to the UK became a British Overseas citizen. British Overseas citizens can not pass on their citizenship to their children, unless their children are stateless.
British Overseas Citizens are unique in that their nationality status is not associated with the right of residence anywhere in the world
http://en.wikipedia.org/wiki/British_Ov ... itizenship
The caveat is she
may have remained a British citizen if her parents were born in the UK. But if the latter were the case, she would be a British citizen by descent and hence unable to pass on her citizenship to you.
Again, most of this information is gleaned from Wikipedia and online resources and as Wanderer said, you are best off consulting an immigration lawyer for professional advice.
Another option, which would require settling in the UK for atleast five years, is to apply for a UK Ancestry visa.