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Can I get a UK passport with form UKM due to this?

I was born in Zambia during British rule but got my passport after they got their independence.

Both my parents however had a UK passport and later settled in England too while I remained in Zambia. However, can I claim for British passport due to descent?

My mum and dad were both born in India during colonial rule but immigrated to Zambia in the 50s; both had a UK passport and later moved to England in 1975.

I checked the required forms with this link: http://www.ukba.homeoffice.gov.uk/briti ... documents/

Could I her British Passport serve proof for the following - "her certificate of naturalisation or registration as a citizen of the United Kingdom and Colonies (or, before 1 January 1949, as a British subject);".

Also, what additional evidence of her service is required?

the basic answer is "no". Because your parents were British citizens by descent, you aren't automatically British yourself.

BUT as they were in a then-colony, you might still qualify yourself. You'd need to have a much more detailed examination of the facts.