LONDON -- The European Union wants a quickie divorce, but Britain wants time to think things over.

Senior EU politicians demanded Saturday that the U.K. quickly cut its ties with the 28-nation bloc - a process Britain says won't begin for several months - as the political and economic shockwaves from the U.K.'s vote to leave, known as Brexit, reverberated around the world.

"There is a certain urgency ... so that we don't have a period of uncertainty, with financial consequences, political consequences," French Foreign Minister Jean-Marc Ayrault said at a meeting in Berlin of the EU's six founding nations.

EU Commission chief Jean-Claude Juncker warned that the split was "not an amicable divorce" but noted it was never "a tight love affair anyway."

Britons voted 52 to 48 percent Thursday in favor of ending their country's 43-year membership in the 28-nation bloc.

But no country has ever left the EU before, so no one knows exactly how the process will play out. Britain must, at some point, unambiguously notify the bloc of its intentions and set a two-year clock ticking for negotiating its departure. Until then, Britain remains an EU member.

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In contrast to the clamoring of EU officials, the leaders of Britain's "leave" campaign, who had reassured voters that the EU would offer Britain good terms for a new relationship, were largely silent Saturday.

CBS News correspondent Jonathan Vigliotti reports some voters said they felt misled by the "leave" campaign, which promised among other things that exiting the EU would free up billions of pounds to be spent on health care in the U.K. But after the vote, pro-Brexit politician Nigel Farage, appearing on national television, admitted that the "leave" campaign made a mistake.

England's 300-year-old union with Scotland could be another casualty of the referendum, since most people in Scotland voted to remain in the EU but were outvoted by a majority in much-larger England.

Scottish leader Nicola Sturgeon said Saturday that her semi-autonomous administration would seek immediate talks with EU nations and institutions to ensure that Scotland could remain in the bloc.

"(We will) explore possible options to protect Scotland's place in the EU," she said after meeting with her Cabinet in Edinburgh, adding that a new referendum on Scottish independence is "very much on the table."

Scotland voted in 2014 to remain a part of the U.K., but that decision was seen as being conditional on the U.K. staying in the EU.

The victorious "leave" campaigners have said there's no rush to trigger Article 50 of the EU's Lisbon Treaty, which will begin a two-year exit process to renegotiate trade, business and political links between the U.K. and what will become a 27-nation bloc.

British Prime Minister David Cameron announced his resignation Friday and said his successor, to be chosen by October, should be the one to navigate the tricky process of withdrawing from the bloc.

The favorite to succeed him, former London Mayor Boris Johnson, has said there's "no need for haste" - but EU leaders are saying the opposite, in insistent tones.

Juncker said Saturday the British had voted to leave and "it doesn't make any sense to wait until October to try and negotiate the terms of their departure."

"I would like to get started immediately," he said.

French Economy Minister Emmanuel Macron expressed the frustrations that many EU politicians feel, accusing Britain of taking the EU "hostage" with a referendum called to solve a domestic political problem: challenges to Cameron from right-wing euroskeptics.

"The failure of the British government" has opened up "the possibility of the crumbling of Europe," Macron said at a debate in Paris.

Top diplomats from the European Union's six founding nations - France, Germany, Italy, the Netherlands, Belgium and Luxembourg - met in Berlin for hastily arranged talks and stressed that the exit process should be speedy.

"There must be clarity," Luxembourg Foreign Minister Jean Asselborn told reporters. "The people have spoken and we need to implement this decision."

France's Ayrault suggested Britain could name a new prime minister within "several days" - but that is likely instead to take several months. The process calls for Conservative lawmakers to winnow candidates down to two choices who will then be voted on in a postal ballot of party members.

Legally, there is little the EU can do to force Britain's hand, since Article 50 must be triggered by the country that is leaving. But political pressure and economic instability may force British politicians to act more quickly than they had hoped.

German Chancellor Angela Merkel struck a conciliatory note, saying it "shouldn't take forever" for Britain to deliver its formal notification of leaving.

"There is no need to be particularly nasty in any way in the negotiations. They must be conducted properly," Merkel said at a news conference in Potsdam, outside Berlin.

Britain's "leave" campaigners have been accused of lacking a plan for the aftermath of a victory.

Dominic Cummings, director of the "Vote Leave" group, said it would be "unthinkable" to invoke Article 50 before a new prime minister was in place. He tweeted: "David Cameron was quite right. New PM will need to analyze options and have informal talks."

Britain will remain an EU member until the divorce is finalized, but its influence inside the bloc is already waning. Leaders of the bloc will hold a summit in Brussels next week, and the second day, Wednesday, will take place for the first time without Britain.

On Saturday, Britain's representative on the EU's executive Commission, Jonathan Hill, stepped down, saying he was disappointed by the referendum result but "what's done cannot be undone."

Juncker transferred Hill's portfolio of overseeing financial services to Latvian commissioner Valdis Dombrovskis - costing Britain a key voice in a sector that is hugely important to London, whose status as Europe's financial capital is threatened by Britain's EU exit.

The referendum has already triggered financial turmoil around the world. Stock markets plummeted Friday, with the Dow Jones industrial average dropping 611 points, or 3.4 percent, its biggest fall since August. It's not clear what will happen in the markets on Monday, the next trading day.

The pound on Friday dropped to its lowest level since 1985, plunging more than 10 percent from about $1.50 to $1.35 before a slight recovery, on concerns that severing ties with the EU single market of 500 million people will hurt the U.K. economy and undermine London's position as a global financial center.

Credit rating agency Moody's downgraded the U.K.'s economic outlook from stable to negative, saying Britain faces "a prolonged period of uncertainty ... with negative implications for the country's medium-term growth outlook."

The vote to leave the EU has upended British politics. The deeply divided Conservatives are facing a leadership battle to replace Cameron, and some members of the opposition Labour Party hope to oust their leader, Jeremy Corbyn, who they accuse of failing to promote the "remain" side strongly enough.

"(Corbyn) clearly isn't the right person to actually lead the party into an election because nobody thinks he will actually win," said Labour legislator Frank Field.

Corbyn said Saturday he would not resign and said Britain must react "calmly and rationally" to the divisive referendum result.