Fast facts about British nationality for South Africans – You could be eligible for British passport if you were:

Born to a parent (father or mother) who was born in the UK before 1983.
Born before 1983 to a parent who was born after 1949 – as long as that parent
Was a British citizen, or
Had a parent born in the UK
Born in South Africa after 31 May 1962 but before 1983, and you have a UK-born grandparent
Born after 1948, and your parents were married before 1949 and your paternal grandfather (your father’s father) was born in the UK
Born between 2 March 1970 and 18 April 1980 in (Southern) Rhodesia, and you have a grandfather born in the UK.