By Brian Wheeler
BBC News politics reporter
A grey lunchtime in London's Trafalgar Square is not, on the face of it, the most promising venue to witness a piece of living history.
Mr Mandela exerts a powerful pull
But that was what as many as 20,000 people who gathered there on Thursday had come to see.
"He is one of my heroes. We had to be here," said Joanna Bryson, a social work student, who like many others had skipped classes to see Nelson Mandela at the Make Poverty History rally.
"You have to come and see Mandela," agreed Christian Aid worker Tom Pugh, 23.
Chris Lawrence, a community worker from Hackney in East London, had brought his two-year-old daughter, Asha. ("It means hope. She was born at the time of the Iraq war").
"I wanted her to see Nelson Mandela, to connect with a whole epoch of history."
Before Mr Mandela's release from prison in 1990, Trafalgar Square was the scene of anti-apartheid demonstrations in front of the South African embassy.
And there has been a vigorous campaign for a statue of the great man to be erected on the square's vacant fourth plinth, a few feet to the left of the makeshift stage he was due to speak from on Thursday.
London mayor Ken Livingstone has backed an alternative plan for a statue to the north of the square.
On Thursday, South African embassy staff crowded on to its balcony, to gain a grandstand view of the crowds in the square and a sea of War on Want, Christian Aid and other banners.
A succession of speakers and warm-up acts, including a troupe of African drummers and young R&B singer Jamelia, were introduced to polite applause by Channel 4 presenter June Sarpong ("come on, make some more noise").
'President of the world'
The crowd were saving themselves for the main attraction, introduced by Bob Geldof as the man "with the coolest shirt collection in the world" and, in a final flourish, "president of the world".
Schoolchildren meet their idol
Mr Mandela, who turns 87 this year, appeared at the top of the stone staircase to wild applause. His journey to the microphone, accompanied by his wife, was slow and unsteady, as he leaned for support on a white walking stick.
But once there he spoke lucidly and with passion, every inch the embodiment of quiet dignity.
Afterwards, he met school children from Glasgow and London, handing them his white Make Poverty History arm band.
Mr Geldof joked that Mr Mandela would hang around all day if he could, and watching him swap jokes with the children and turn one last time to wave and smile at the crowd before climbing into his waiting car, you could believe it.
"I was very moved by the speech", said Lillian Ricketts-Hagan, a 36-year-old Ugandan studying at the London School of Economics.
"If Nelson Mandela is not going to fight for our cause, who else is? Tony Blair perhaps, but it is only because he has people like Nelson Mandela pushing him."
Law student Unyime Davies, 21, said: "He was awesome. We are still quite awestruck. You could not believe he was actually there."
Her friend Stephen Lue, 20, said: "He was older than I expected. I didn't expect him to be so fragile.
"But whatever he says you have to listen because he is genuine. He is one of the most genuine people you can think of. History speaks for itself."
But will the world's leaders listen to him when he addresses G7 finance ministers on Friday?
"If they won't listen to Nelson Mandela who are they going to listen to?," Ms Davies said.
"It would almost be like telling your grandfather he is wrong. They will argue about the logistics and the economics. He will be the conscience of the meeting."