The world is facing "the first truly global financial crisis", the prime minister has told leaders.
Gordon Brown said institutions such as the World Bank and United Nations need reform to tackle the double threat of economic turmoil and climate change.
He is hosting the two-day gathering in Watford attended by delegates including ex-US president Bill Clinton and Australian PM Kevin Rudd.
Topics including climate change and development will be on the agenda.
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Mr Brown and Mr Mbeki are due to hold one-to-one talks at some point on Saturday, with the election in Zimbabwe likely to feature heavily in discussions.
Arriving at the summit, Mr Mbeki said the international community should await the results of last Saturday's poll.
"It's time to wait and see the outcome of the election results. If there's a re-run of [the] presidential election, let's see what comes up with that," he said.
"That's the correct way to go."
The UK prime minister has already spoken to the leaders of Ghana and Liberia about the situation in Zimbabwe.
'Early warning system'
Speaking at the start of the Progressive Governance conference of centre-left leaders and politicians, Mr Brown said that the old institutions established in the aftermath of World War II were now unable to cope.
"We now have to reshape our global rules and global institutions for this new era," he said.
"We are facing a global financial crisis which is probably the first truly global financial crisis of the modern world.
"We have to reform our global financial institutions. It is absolutely clear that the national supervision that we have is inadequate and we need a global agreement."
The prime minister said the International Monetary Fund (IMF) needed complete re-structuring so it could act as an "early warning system" for the international economy.
He said the World Bank should help developing nations move towards cleaner economic development.
Mr Brown also suggested there should be an international reserve force of volunteers ready to help rebuild countries such as Rwanda and Bosnia following global crises.
(BBC)
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