(Adds Asia markets, Osborne ruling out standing for PM, S.Korea supplementary budget, England soccer loss)
* British economy "as strong as it could be" - Osborne
* British ruling party and opposition both in crisis
* Sterling and world shares fall again, U.S. urges calm
* EU wants quick resolution
By Kylie MacLellan and Anirban Nag
LONDON, June 28 (Reuters) - Britain's vote to leave the European Union continued to reverberate through financial markets, with the pound falling to its lowest level in 31 years, despite government attempts to relieve some of the confusion about the political and economic outlook.
UK finance minister George Osborne said early Monday that the British economy was strong enough to cope with the market volatility caused by last week's "Brexit" referendum which has resulted in the biggest blow since World War Two to the European goal of forging greater unity.
"Our economy is about as strong as it could be to confront the challenge our country now faces," Osborne told reporters.
"It is inevitable after Thursday's vote that Britain's economy is going to have to adjust to the new situation we find ourselves in," said Osborne, who later ruled himself out of the running to succeed David Cameron as prime minister.
Boris Johnson, a leading proponent of Brexit and the frontrunner to be the next prime minister, praised Osborne for saying "some reassuring things to the markets".
The former London mayor said it was now clear that "people's pensions are safe, the pound is stable, markets are stable. I think that is all very good news."
But neither Osborne's nor Johnson's words failed to stop the slide in stocks on world markets which began last Friday when Britons confounded investors' expectations by voting to end 43 years of EU membership.
European bank shares had their worst two-day fall on record and world stocks as measured by MSCI index saw their worst two-day fall since the collapse of U.S. investment bank Lehman Brothers during the 2008 financial crisis. On Friday alone about $2.8 trillion was wiped off the value of world stocks, the biggest daily loss ever.
Sterling fell to a low around $1.3120, its lowest level since mid-1985. The euro also remained weak, after falling to a three-month low around $1.0910 on Friday.
Asian stocks markets opened weaker on Tuesday, with MSCI's Asia ex-Japan index extending losses for a third day, down 0.5 percent. Japan's Nikkei was off 0.7 percent.
"Markets already appear to be pricing in a full-blown recession in the U.K. and rising recession risk in the rest of Europe," said David Donabedian, chief investment officer of Atlantic Trust Private Wealth Management.
Ratings agency Standard & Poor's stripped Britain of its last remaining top-notch credit rating on Monday, warning that more downgrades could follow.
"In our opinion, this (referendum) outcome is a seminal event, and will lead to a less predictable, stable, and effective policy framework in the UK," S&P said in a statement.
The yield on British 10-year government bonds fell below 1.0 percent for the first time as investors bet the Brexit vote would trigger a Bank of England interest rate cut aimed at steadying the economy.
U.S. stocks ended lower for a second day also, following European markets, pulled down by banking stocks amid uncertainty over London's future as the region's financial capital. Safe-haven bond and gold prices rose.
U.S. Treasury Secretary Jack Lew on Monday said he sees no signs of a financial crisis arising from Britain's decision last week, although he admitted that the result does present additional "headwinds" for the U.S. economy.
Visiting Brussels, U.S. Secretary of State John Kerry said it was important that "nobody loses their head" as the EU and Britain deal with the fallout from the referendum.
European Central Bank President Mario Draghi expressed "sadness" on Monday at Britain's vote to leave the European Union.
Draghi will fly to Brussels on Tuesday, where he is expected to brief European leaders about the impact of the UK vote on the euro zone at a two-day European Council meeting.
POLITICAL CONFUSION IN BRITAIN
With the ruling U.K. Conservative party looking for a new leader after Cameron's resignation on Friday and lawmakers from the opposition Labour party stepping up a rebellion against their leader, Britain sank deeper into political chaos.
"There's no political leadership in the UK right when markets need the reassurance of direction," said Luke Hickmore of Aberdeen Asset Management, expressing the view of many in the City of London financial centre.
British broadcaster Sky News said work and pensions minister Stephen Crabb was also considering a bid for the Conservative party leadership, with business secretary Sajid Javid seeking to become finance minister. Both were in favour of staying in the EU. The editor of the Spectator magazine tweeted that Health Secretary Jeremy Hunt was also "highly likely" to launch a bid.
Cameron says he will stay on until October as a caretaker and that his successor should trigger the formal process of leaving the EU. His Conservative Party in parliament recommended choosing a successor by early September.
The prime minister sought to calm fears over the fallout of the referendum and said parliament should not try to block Britain's departure. A majority of parliamentarians, like him, had argued that Britain should stay in the EU.
"I am clear, and the cabinet agreed this morning, that the decision must be accepted," Cameron told parliament, which also faces a public petition for a new referendum.
While the question of whether to leave the EU has split the ruling Conservative party, divisions within the opposition are also deep. A wave of Labour lawmakers resigned from leader Jeremy Corbyn's team on Monday, adding to the 11 senior figures who quit on Sunday, saying his campaign to keep Britain in the EU was half-hearted.
Corbyn, a left-winger who has strong support among ordinary party members, has said he is not stepping down.
Discontent with the political establishment in general and the Conservatives in particular was a factor behind the vote to leave, although many Brexit backers focused on immigration, complaining too many migrants had arrived from eastern Europe.
Piling on misery for beaten English "remain" voters, the country's soccer team on Monday crashed out of the Euro 2016 soccer competition to tiny Iceland.
"We embarrassed ourselves three of four days ago in the referendum, we've embarrassed ourselves now. It's a really, really sad time to be English," lamented English soccer fan Alex in the French city of Nice.
EUROPE WANTS QUICKER RESOLUTION
Cameron's refusal to start formal moves to pull the country out of the EU has prompted many European leaders to demand quicker action by Britain, the EU's second largest economy after Germany, to leave the 28-country bloc.
"It should be implemented quickly. We cannot remain in an uncertain and indefinite situation," French Finance Minister Michel Sapin said on France 2 television.
Guenther Oettinger, German member of the EU's executive European Commission, said delay would hurt Europe as well as Britain. "Every day of uncertainty prevents investors from putting their funds into Britain, and also other European markets," he told Deutschlandfunk radio.
Cameron heads to Brussels on Tuesday for a grim EU summit dinner, while the other 27 leaders will meet for the first time without him on Wednesday morning to plan their next moves. They are likely to stress a willingness to negotiate, but only after London binds itself to a tight two-year exit timetable.
The leaders of France, Germany and Italy met in Berlin on Monday and said Europe needed to respond to its people's concerns by setting clear goals to improve security, the economy and prospects for young people.
German Chancellor Angela Merkel, who has appeared to take a softer line on Britain's decision than some European leaders, said she had "neither a brake nor an accelerator" to control events, adding: "We just don't want an impasse."
The political, economic and regulatory uncertainty is being felt across the globe at a time when economies are still slowly recovering from the 2008 economic crisis, interest rates are close to zero, and central banks have fewer tools than normal to revive demand if countries enter recession.
South Korea said on Tuesday it would propose a supplementary budget of around 10 trillion won ($8.44 billion), in part to help it manage Brexit turmoil in financial markets.
(Additional reporting by David Lawder, William James, Jamie McGeever, Nigel Stephenson, Kevin Yao, Costas Pitas, Bate Felix, Andrea Shalal, Michael Holden, Guy Faulconbridge, David Milliken, Patrick Graham, Michelle Martin, Elizabeth Piper, Paul Carrel, Conor Humphries, Minami Funakoshi and Tetsushi Kajimoto.; Writing by David Stamp, Philippa Fletcher and Lincoln Feast.; Editing by Peter Graff, Andrew Roche, Kevin Liffey, Clive McKeef)
