Shares in London and across the world shot ahead tonight amid hopes of a deal by world leaders at the G20 summit.

The FTSE 100 index shot up 136.71 points, or more than 3%, to 4092.32, the first time it has been above 4000 for six weeks, on tentative hopes that stability was returning to the global economy and the worst of the downturn may have passed.

Shares were also on the rise in Europe, Asia and the US as Gordon Brown met heads of state from the G20 nations to thrash out a plan for restoring growth and rebuilding the battered financial system.

The oil price soared amid hopes of an end to the economic gloom, with London Brent crude up $3.94 a barrel to $52.38.

“A good rally is coming through on hopes for a decent stimulus package from the G20 to lift confidence, especially with regard to emerging economies and a boost to the International Monetary Fund,” said Henk Potts, analyst at Barclays Wealth.

However, there was disappointment when the European Central Bank lowered interest rates by less than expected, from 1.5% to 1.25%, despite signs that recession in the eurozone is deepening.

“It sends the signal that they don't mean business and continue to be behind the curve,” said Philippe Gijsels, a strategist at Fortis in Brussels. “A cut of only 25 basis points indicates that there is not much urgency.”

ECB president Jean-Claude Trichet this evening said it was ready to cut further “in a very measured way” but that was still not seen as enough by investors.

The claim that Europe is slow to react piled pressure on German Chancellor Angela Merkel and French president Nicolas Sarkozy, who have vigorously disagreed with spending plans proposed by US President Barack Obama.

City analysts warned the stock market rally could be short lived if the G20 summit fails to come up with firm proposals, or the recession takes a turn for the worse. Although the Footsie is up 15% from its low last month, it is 9% down this year.

Joshua Raymond, market strategist at City Index, said: “This is indicative of how volatile the markets are and how quickly trading appetite can change. These violent swings are likely to continue, particularly if the G20 summit disappoints and investors look to consolidate.”

The world economy looks set to shrink this year for the first time since the Second World War as tens of millions of people lose their jobs in developed and developing countries.

The G20 pledged to deliver “the scale of sustained effort necessary to restore growth” and declared an end to unfettered capitalism.

Hedge funds face regulation for the first time and bonus payments look set to be curbed, factors that could hit tens of thousands of workers in London.

Multi-million-pound bonuses paid to bankers have been blamed for encouraging banks to take “reckless” decisions that triggered the global financial crisis, and France and Germany have pushed for limits to be imposed.

German finance minister Peer Steinbrück said: “In my view, the most important issue is that we agree, also with the British and the Americans, on the principle that no financial market product, no financial market participant and no financial market can remain without regulation and without supervision. That is the actual message.”