The other Nelson towers over Trafalgar Square

Not only did he have the coolest collection of shirts on the planet, said Sir Bob Geldof, performing the introductions in Trafalgar Square yesterday, but as far as he was concerned, this was a man who could rightly be called President of the World.

And, Sir Bob made clear to the assembled throng, it needed the influence of such a man as Nelson Mandela to persuade the richest countries of the world that they should end global poverty.

With that, his shirt of the day unfortunately covered with a voluminous coat but wearing a jaunty fur hat, the 86-year-old Mr Mandela came to the microphone to be greeted with a bear hug from Sir Bob and a huge cheer from the crowd, estimated at about 20,000.

"Like slavery and apartheid, poverty is not natural," Mr Mandela told the rally, organised by the Make Poverty History campaign and timed to coincide with the meeting of the G8 finance ministers in London this weekend; Mr Mandela will meet them tonight.

Trafalgar Square was the scene of many anti-apartheid rallies during the 1970s and 1980s when Mr Mandela was imprisoned by the South African regime. In those days, South Africa House was ringed by police. Yesterday, its windows and balconies were packed with those eager to see and hear their former president, who last spoke there in 2001.

Thanking British people for their support against apartheid, Mr Mandela said: "In this new century, millions of people in the world's poorest countries remain imprisoned, enslaved, and in chains. They are trapped in the prison of poverty. It is time to set them free. Overcoming poverty is not a gesture of charity. It is an act of justice. It is the protection of a fundamental human right, the right to dignity and a decent life. While poverty persists there is no true freedom." Mr Mandela may have looked frail and walked with the aid of a stick but his voice and his message were strong and firm: Poverty and obscene inequality were the "terrible scourges of our times", he said, adding: "This is unforgivable in an age when the world boasts breathtaking advances in science, technology, industry and wealth. They have to rank alongside slavery and apartheid as social evil."

Reminding his audience of the Millennium Declaration made by world leaders in 2000 to end extreme poverty, Mr Mandela said: "The promise is falling tragically behind.'' He also urged people to bring pressure on the G8 leaders, who meet in Scotland in July, to honour their pledge to focus on poverty. Mr Mandela exchanged white armbands - the symbol of the campaign - with a group of children.

Sir Bob, the warm-up act, was typically impassioned. For years, he said, Trafalgar Square was where people had spoken out for sanity, dignity and justice. "And here we are again,'' he said.

Despite the contribution of this year's Band Aid record of $30m (£16m) it was only politicians, he said, who could unravel the "barbed tangle of poverty, unjust trade, debt and corruption". Sir Bob declared: "I'm tired of the politics of being nice, I want the politics of responsibility. I'm sick of standing in squares and linking arms in foreign cities, of tear gas and of the pop concerts and records. I'm sick of this crap." The world's leaders, he said, "must be persuaded to do what they are paid for; they must enable the world we wish to create".

Mr Mandela was taken by car a few yards to South Africa House for a reception in his honour. Perhaps, as Sir Bob said, this is a man whose very presence can make a difference.