A summit was held between Mrs Thatcher and PW Botha in 1984 - the only such meeting between the two leaders - to discuss the country's policy towards its black population.
Mr Mandela, who died last month, was at the time in Pollsmoor Prison and had become an international symbol of opposition to apartheid.
But Mrs Thatcher did not mention Mr Mandela's detention in the official discussion with Mr Botha, choosing instead to raise the issue during a short pre-meeting held without note-takers.
According to the late PM's own description of the event, Mr Mandela's plight was "noted" only during a private audience requested by South Africa to discuss "sensitive issues".
In a report, Number 10 confirmed the issue was raised at a short "tete-a-tete" with little success. Adviser John Coles wrote on June 2 1984: "The Prime Minister said afterwards that Mr Botha had stated that it was never possible for South Africa to satisfy international opinion. She took the opportunity to raise the case of Nelson Mandela. Mr Botha said he noted the Prime Minister's remarks, but that he was not able to interfere with the South African judicial process."
In the officially minuted meeting that followed, Mrs Thatcher omitted their disagreement over Mr Mandela - despite Foreign and Commonwealth Office guidance to make the point.