Your grandfather is what is called “British otherwise than by descent”. That means he was a British citizen born or naturalised in the UK.

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Your mother is what is called “British by descent”. That means she was born abroad to a person who was British otherwise than by descent.

British citizenship is normally only transmitted one generation outside the UK, meaning your mother is the end of the line.

Original Source: https://www.quora.com/Can-I-apply-for-British-citizenship-if-my-grandfather-was-born-in-the-UK-but-my-mother-his-daughter-was-born-abroad-and-also-myself/answer/My-Legal-Services-1