London (CNN)Not since World War II has Britain faced such an uncertain future.

A vote last week to pull out of the European Union has left Britain with a nasty hangover, sending the currency spiraling, dampening markets, creating a leadership vacuum and triggering talks of Scottish secession from Britain, forcing the government into damage control.

But the divorce is already looking messy, with Prime Minister David Cameron and key EU leaders in disagreement on how to even begin.

Cameron, who resigned after the vote and plans to step down in October, said he would not yet officially inform the EU of Britain's withdrawal from the bloc.

"Before we do that, we need to determine the kind of relationship we want with the EU," he said. "Any new negotiation to leave the EU will begin under a new prime minister."

But German Chancellor Angela Merkel made clear that Britain's official notice must come first, which involves invoking a clause in the treaty that binds the union.

"We cannot start some sort of informal talks without having received the notice from Great Britain. This is very clear to me," she told journalists in Berlin on Monday as EU leaders huddled ahead of a major meeting in Brussels. U.S. Secretary of State John Kerry will also attend, although Cameron is not expected to take part in much of the session.

She said the EU does "not want a stalemate." "But we have to be sure we are not hanging in the balance, and the first step must be taken by Great Britain," she said.

French President Francois Hollande and Italian Prime Minister Matteo Renzi agreed with Merkel, saying Britain must "waste no time" to get the separation started.

Opposition Labour Party leader Jeremy Corbyn, who backed Britain remaining in the EU, said stalling the announcement would leave Britain in "a state of paralysis," delaying for months what could be a two-year separation process, potentially followed by more years of trade talks.

But Corbyn faces political paralysis of his own, and his Labour Party is offering no more certainty to the British public than the ruling Conservatives.

Nineteen Labour Party MPs have resigned from senior posts in an act of no confidence in the divisive leftist leader.

Cameron was quick to jump on fallout from an attempted Labour Party coup, appearing chirpy despite the failure of his campaign to keep Britain in the European Union.

"And I thought I was having a bad day," he joked in Parliament of Corbyn's leadership problems.

Broken promises

Like the markets, Brits are jittery, not knowing who will lead their country come October or whether any of the promises made by the leave camp will even come into fruition.

Leave campaigners are already back-pedaling on their promises, and many who voted to leave say they feel cheated, and regret their vote.

The leave camp said pulling out of the European Union would save Britain £350 million a week, money that could be poured into the country's stretched National Health Service. Now they are saying they can't guarantee that would actually happen.

In fact, nothing will change until Britain invokes Article 50 of the Lisbon Treaty.

Who's in charge?

Cameron announced in parliament that a new unit would be established to deal specifically with the EU divorce in what he described as one of the "most complex" tasks assigned to the civil service in decades.

It would bring together members of various bodies and services, including the cabinet office, the foreign office and the Treasury, among others.

Earlier a spokeswoman from the prime minister's office said that Oliver Letwin, one of Cameron's influential policy advisers, would lead the unit.

Letwin is an old friend of Cameron's from Eton College. Cameron had come under criticism for peppering his cabinet with old school friends from the expensive institution.

U.S. Secretary of State John Kerry said that the vote would not change Washington's "unbreakable bond" with Britain.

"We believe our relationship remains as strong and as crucial as ever," he said at a joint press conference in London with British Foreign Secretary Philip Hammond.

Hammond said that vote was "damaging to Britain" but also "damaging for the European Union," arguing that both Britain and EU would have been enhanced if the people voted to remain in the bloc.

'Open for business'

Leaders are now trying to allay fears that Britain may be heading for recession and are trying to boost confidence in its markets and currency to avoid an economic meltdown.

Cameron reminded parliament that Britain has "one of the strongest major advanced economies in the world."

But the country just lost its top AAA credit rating with agency Standard & Poor's, which measures a country's ability to meet its financial commitments.

"In the nationwide referendum on the U.K.'s membership of the European Union (EU), the majority of the electorate voted to leave the EU. In our opinion, this outcome is a seminal event, and will lead to a less predictable, stable, and effective policy framework in the U.K.," S&P said in a staement.

"The vote for 'remain' in Scotland and Northern Ireland also creates wider constitutional issues for the country as a whole," it said.

But Cameron assured the world that Britain was "well placed to face the challenges ahead. The [central] bank's stress tests show that UK institutions have enough capital and liquidity reserves to withstand a scenario more severe than the country currently faces."

Cameron's comments echoed those of UK Treasury chief George Osborne, who said earlier that the economy remained "fundamentally strong."

"To companies, large and small, I would say this: the British economy is fundamentally strong, highly competitive and we are open for business."

But the shock outcome of the Brexit vote pushed the British pound down to its lowest leve in around three decades, and hit the country's markets hard.

The pound was down to 1.31 to the dollar by the afternoon and London's FTSE 250, which is made up of mostly mid-sized British companies, closed 7% lower Monday.

Former London mayor and prominent leave campaigner Boris Johnson -- tipped as a favorite to stand in for Cameron as prime minister -- welcomed Osborne's decision not to make any changes to the budget until after a new prime minister is installed. He said "project fear" is over, referring to what he said was economic fear-mongering from remain campaigners trying to keep Britain in the bloc.

But Adam Marshall, Acting Director General of the British Chambers of Commerce, said that businesses wanted a clear timetable for exit.

"While it is prudent for the UK government to delay firing the starting gun on negotiations with the European Union, firms want a clear timetable, and simultaneous action to support the wider economy," he said.

Labour's own meltdown

The jockeying for power is not exclusive to Cameron's Conservative Party. Labour MPs have seized the Brexit turmoil to try to oust party leader Corbyn, who has taken the party in a new direction after two consecutive election losses to the Conservatives.

Corbyn is a divisive figure among Labour MPs -- his leftist economic vision is seen as radical, including salary caps and nationalization of essential services like public transportation.

But he is popular among Britain's left. He has brought tens of thousands of new members to the party and an attempt to oust him could easily backfire, as party members across the country could easily vote him back in should his leadership be officially challenged.

Labour MPs argue that Corbyn is popular but not realistically electable, and could keep the party in the political doldrums for years to come.

On Monday, Corbyn announced a new-look "shadow" cabinet, following the resignations of senior party members from their positions.

Britain's main opposition party typically creates a shadow cabinet mirroring the party in power. Shadow ministers are assigned portfolios, and it is their job to challenge cabinet ministers on specific issues.

By the late afternoon, 19 of these shadow ministers had resigned. Shadow Foreign Secretary Hilary Benn was given the boot after he was accused of being behind the leadership coup against Corbyn that is still simmering.

Labour confirmed 10 new appointments, including key allies Diane Abbott as shadow health secretary and Emily Thornberry as shadow foreign secretary to replace Benn. While his parliamentary colleagues are set to discuss a no confidence motion against Corbyn, the beleaguered leader has stated that he will stand in any future leadership contests.

"Those who want to change Labour's leadership will have to stand in a democratic election, in which I will be a candidate," he said.

Critics within his own party have criticized Corbyn's lukewarm campaigning for the UK to remain within the EU, and suggest the blame for the country's exit should at least partially fall on his shoulders.

At the time of writing, an online petition to retain Corbyn as leader had garnered just over 200,000 signatures.

Boris Johnson: Time for unity

In his regular Sunday Telegraph column, leave campaigner and potential future prime minister Boris Johnson sought to reassure Britain that the country remains "a part of Europe, and always will be" following Thursday's EU referendum.

Writing his first opinion piece in the pro-Leave Telegraph since the so-called "Brexit" poll determined that a majority of voters wished to end the UK's 43-year membership in the European project, Johnson sought to reassure "Remain" voters and the markets.

"We who are part of this narrow majority must do everything we can to reassure the Remainers," he wrote.

"We must reach out, we must heal, we must build bridges -- because it is clear that some have feelings of dismay, and of loss, and confusion."

Renewed calls for Scotland to secede

Following the seismic vote, Scotland's First Minister Nicola Sturgeon has suggested that the Scottish Parliament could yet veto the decision, the BBCreports, though the Conservative Party has rejected the idea. Sturgeon earlier said that a second independence referendum for Sctoland was very possible should Britain's EU divorce become official.

On Sunday she said that she would "of course" ask her party's members to refuse to give their "legislative consent" for the EU separation and that it would be "democratically unacceptable" for Scotland to lose its EU membership after voting 62% to remain. She said she would initiate talks with Brussels in the coming week about Scotland remaining in the EU.

Global economic shockwaves

The Brexit effects are still being felt around the world. In the U.S., the Dow dropped 258 points in the early afternoon and U.S. financial stocks took a hammering.

Europe's markets closed deep in the red, with the Irish Stock Exchange losing a steep 9.5% and Germany's DAX dropping 3%.

But some markets further afield appear to have weathered the storm. Japan's Nikkei 225 closed up 2.39%, recovering some of Friday's steep losses, while Australia's S&P ASX 200 finished up 0.47%.

Delivering opening remarks at the World Economic Forum in Tianjin, China, Chinese Premier Li Keqiang said that the impact of the vote was being felt worldwide and would increase global uncertainty and make it more difficult for the global economy to rebound. He added that stability for both the bloc and the breakaway UK was important to shore up the global economy.

"Europe is an important partner of China. China will keep preserving and developing both China-EU and China-UK relations. We hope to see a united and stable EU as well as a stable and prosperous UK."