The meeting will be led by eight "sherpas", the chief officials from the G8 leading industrialised countries charged with preparing the communique for world leaders to sign at the summit in Gleneagles next Friday. Sitting behind them will be their assistants, known in this corner of officialdom as sous-sherpas.
Acting under the policy parameters set by their political masters, these people will in effect decide whether the songs in the park just a mile away will be sung in vain.
The sherpas will have been meeting since Friday. Their job is to move words and phrases in and out of square brackets. If a phrase stays in square brackets, it is not agreed. If it comes out of brackets, consensus has been reached. So it is not too melodramatic to say that the removal or insertion of brackets is not just a piece of dry diplomatic craftwork - it may save not just individual lives, but even species.
At the moment British officials admit that too much on both Africa and climate change remains in brackets. Progress has been so slow over the past few months that Tony Blair's officials decided to call the extra meeting in London this weekend to try to force a breakthrough: the coincidence with Live 8 was not accidental.
In the British seat at the table is Michael Jay, permanent secretary at the Foreign Office and former ambassador to France. He has said he has not seen a G8 negotiation of such intensity for more than a decade.
Unlike most G8 communiques, Mr Blair is looking for this text to include specific sums for programmes, such as extra cash for malaria, an extra $3bn for girls' primary education and water management, and an additional $10bn a year funding for infrastructure by 2010.
British officials have been told by Mr Blair not to give way, and over the last week the UK's delegation has been furiously hitting the phones to their G8 colleagues.
Much of the traffic is directed at Washington and the White House. Even those closest to the negotiations in Britain admit that at this 11th hour they do not know if and what Mr Bush will decide. The auguries are not good.
In the case of Africa, the officials have tried to frame the wording along the lines of the bold Commission for Africa report published in the spring, chaired by Tony Blair, and on which many leading African politicians sat. At its heart was a commitment to an extra $25bn a year in aid to Africa as part of a "go for growth strategy". Mr Blair, the chancellor Gordon Brown and the international development secretary, Hilary Benn, plumped for the ambitious tactics of first securing a hard-fought deal on multilateral debt at the G7 finance ministers' meeting in April, relieving Africa in theory of $1.5bn debt repayments annually. This left them six weeks to press for agreement on the big aid package.
No 10 has not given up hope, but it is admitted that it has been a struggle to get President George Bush to focus on the issue. The evangelical right cares about Africa. So does Condoleezza Rice, the state secretary. On the other hand the Senate recently cut the US aid budget.
One confidante said Mr Blair in his visit to the White House last month to discuss his G8 agenda found Mr Bush far more exercised by Iraq than by either climate change or Africa. One official thought Mr Bush might have gone backwards since his previous meeting with Mr Blair in the autumn. "He sounded like he had been briefed by Vice-President Cheney for 30 seconds on the way in," said one close to the talks.
On Africa Mr Bush's line of defence is that, in comparison with the Clinton administration, he has trebled the aid programme to sub-Sahara Africa to $3.2bn in 2004, set up the millennium challenge account to help the poorest countries, and also poured money into his Aids programme. No 10 has long learned not to criticise the US president in public. But the Brookings Institution, an independent thinktank, this week asserted there has been no tripling of aid, but instead in real dollar terms only an increase of 56%.
British negotiators are finding it difficult to get agreement on specific programmes because other G8 countries are wary about the overall costs. Britain had hoped that an EU pledge by member states to increase its overseas aid budgets to 0.7 % of GDP by 2015 would spur similar action from the Canadians, Japanese and even the US.
The word from the White House is that Mr Bush is willing to offer more aid, but he has been slow to focus. Senior officials have been dispatched to Africa to look at anti-malaria programmes and a scheme for young girls' education. The new head of the World Bank, Paul Wolfowitz, a former administration hawk over Iraq, is also putting his shoulder to the wheel to prepare an infrastructure-based programme that the White House and the private sector could support.
On climate change the progress will be modest, a promise of more technology transfer to the developing world, and a new dialogue between China, India, the US and the EU on energy saving and climate change. The relative absence of progress on this issue will put even more pressure on Mr Blair and his loyal sherpas to achieve some dramatic results on Africa.
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