The tribute to Mandela coincided with disputed elections in Zimbabwe, and during his trip to Britain Mandela was urged to speak out against President Robert Mugabe who pushed ahead with the vote despite international outcry.
Opposition leader Morgan Tsvangirai boycotted the poll because of a wave of deadly attacks on his supporters.
During his visit, Mandela uttered just four words of criticism of Zimbabwe in a speech at a dinner - "tragic failure of leadership" - and they were enough to make headline news.
Mandela, South Africa's first black president, officially retired from politics nine years ago, but he is still a moral authority admired the world over.
People in the crowd appeared to be at the gig more to honour Mandela than to hear the music.
"I'm here because of the man," said Clive Jones, a 31-year-old theatre technician. "I feel he's done so much for the world, especially with what was happening in South Africa. He is also humble and kind."
Emmanuel Jal, a Sudanese hip-hop artist based in London who sang on Friday, said Mandela was "unique" among African leaders. "He did not love power so much, and left it and gave it to someone else," he told Reuters.
Grammy-winning soul singer Winehouse performed her hit single "Rehab" as well as "Valerie", despite being diagnosed with a "touch of" lung condition emphysema earlier this month.
Sporting her trademark black beehive hair, a black and white dress and high-heeled shoes, the 24-year-old appeared nervous at first but received one of the biggest cheers of the night.
At the close of the concert she was joined on stage by Jerry Dammers, who helped organise the 1988 concert, and many of the other performers.
Accompanied by a raucous audience, they sang Dammers' "Free Nelson Mandela", which became an anthem for the anti-apartheid movement in Britain in the 1980s.
