Links via UK Home Office:
Applicants born before 1983 to British mothers (about fee)
and about eligibility for a British passport via DirectGov, website of the UK government:
If you have a British mother
You may have heard about legal changes giving British nationality to people born overseas before February 1961 whose mothers were born in the UK.
If this change affects you, you will need to register with the UK Border Agency before you can become eligible for a passport.