Prior to January 1, 1983, UK citizenship transmitted through descent from British parents to their children born outside of the UK only through the father. Therefore, if you were born to a British mother prior to 1983, you could not claim your UK citizenship.
However, the UK has changed its laws, allowing the children of British mothers born prior to 1983 in countries other than the UK to become citizens. The process is called “registration” because you would not have been considered a UK citizen at your birth, prior to the change in law, and the UK authorities do not have a record of your citizenship. Before you can apply fora UK passport, you must register on the rolls of citizenship.
Once you have registered for UK citizenship, you can apply for a UK passport.
Registration costs £80 and that fee is completely separate from your passport application fee you will have to pay later on.
The processing time can be anywhere between 4 and 6 months. The government has to investigate your case and this involves contacting different countries to verify your records, and this is usually done by mail, which is why it takes so long for you to register.
Once you have registered as a British citizen, you can apply for your first UK passport. That process will take another month or two so, so the total processing time you are looking at could be anywhere between 6 and 8 months, depending upon where you were born and what kinds of records the UK authorities need to consult.
And once you’ve done that, you can apply for a British passport: