She later signed the guestbook open to all visitors, writing: “It has been a privilege to visit in this year – the 100th anniversary of the birth of Nelson Mandela.
“His legacy lives on in the hopes and dreams of young people here in South Africa and around the world.”
Two square mile Robben Island – Dutch for ‘seal island’ – lies about four miles off Cape Town and Mr Mandela was held there until 1982 with other anti-apartheid campaigners put to hard labour.
Mrs May was helicoptered there on the first day of her visit to Africa.
Ahead of her visit, Mrs May was challenged by an interviewer over her failure to protest in the Seventies and Eighties at Mr Mandela’s incarceration by the apartheid South African government.
Channel 4 News repeatedly asked if she felt “guilty” for not doing more at the time.
She said: “What I will be feeling when I go to Robben Island is to recognise the immense statesmanship of a man who spent so many years incarcerated and when he came out of that incarceration had that breadth of vision and that calm approach that has enabled South Africa to be built into the country that it is today.”
Asked if she went on any protests at the time, she said: “I think you know full well that I didn’t go on protests.
“But what is important is the work that the United Kingdom government did to ensure that it was able to give support where that support was needed.
“What is important was the support that the UK government was giving at the time. Often support behind the scenes, but in other ways too, to ensure that we saw the result that we did in relation to the ending of Apartheid.”
Earlier in her speech in Cape Town on building new trade partnerships between the UK and Africa, Mrs May paid fulsome tribute to Mr Mandela and his “walk to freedom” for a just society. He was eventually released by the South African government in 1990.