Hi, I am going through the same process now, British Citizenship by descent for both of my children ....I got both of my children registered at the British Embassy and birth certificate issued for them. (this is all you need and the cheapest method) it's the same documents you need for a passport. Passport is the other method
Please be warned ......the Embassy does not issue passports anymore, so you do not need to print off the C2 form anymore, it's all done from the uk passport office now online. Here are the links below. If you have any questions on the documents you need to send pm me as I have called the Passport Office a few times, you need to have more documents and it's got harder.
http://www.gov.uk/overseas-passports...united-kingdom
https://www.gov.uk/government/public...uments-group-3
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