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It depends on the airline. Some airlines require passports and if the only passport you have is South African, then you also need a visa to go with it.
However, not all transportation operators between Ireland and the UK require passports for British citizens -- several other forms of ID/documentation can also suffice. There's a (non-authoritative, possibly inaccurate) list at Wikipedia.
There shouldn't be any immigration control on arrival in London, due to the Common Travel Area.