The U.K. is in crisis Monday following its decision to leave the European Union with a lack of leadership in both main political parties and no real plan as to who is going to do what next. Following Thursday's referendum, in which 51.9 percent of U.K. voters chose to leave the EU, the British political establishment has been thrown into chaos. This is the scariest thing about the decision to leave: It feels like nobody is in charge right now, and there is no plan for what happens next.

Here is where the aftershocks are hitting. Prime Minister David Cameron, who campaigned for Britain to remain a part of the bloc, announced his resignation soon after the results became apparent but said he would stay on until October in a bid to offer some semblance of stability at a time of market turbulence and uncertainty.

Perhaps suffering one of the longer Brexit hangovers, Chancellor George Osborne waited nearly four days to issue a statement early Monday designed to reassure markets that went into panic mode on Friday with the pound falling to a 30-year low.

Conservative crisis

On Monday, sterling was trading at $1.3164, down around 3.77 percent from Friday's close. It was down around 1.20 percent against the euro. The London FTSE 100 index was trading 2.15 percent lower and some of the turbulence seen at a global level abated.

Nonetheless, there has been no clear message from the government on the next steps in negotiating the U.K.'s exit from the EU, with European leaders pushing for a quick enactment of Article 50 — which would begin the process of extracting Britain from the EU.

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Meanwhile, debates over who will be the leader of the Conservative Party, and therefore prime minister, are already centered over whether he or she should be from the remain or leave camp. Leave campaigner and former London Mayor Boris Johnson, who is believed to have harbored leadership ambitions for some time, is expected to run for the job. Those from the remain camp are also expected to run, casting more doubt over how a British exit from the EU could work. Home Secretary Theresa May and Business Secretary Sajid Javid have also emerged as potential candidates for the Tory leadership. After a Cabinet meeting Monday, Cameron said: "The British government will not be triggering Article 50 at this stage." Some European leaders wanted Britain to immediately invoke Article 50, which would start the two-plus-year process of withdrawing from the EU. "This is our sovereign decision and it will be for Britain, and Britain alone, to take," Cameron said.

Labour in limbo

The Conservative Party is not the only one feeling the heat after the vote: The left wing leader of the Labour Party facing an open revolt from his shadow Cabinet and vote of no confidence on Monday.

Jeremy Corbyn is accused of conducting a lackluster campaign to persuade Labour voters to vote to remain in the EU. Large swathes of the traditional Labour heartland — former industrial towns and cities predominantly in the north of England — voted to leave the EU on Thursday. Also voting with their feet, 12 members of Corbyn's top team resigned this weekend following the sacking of Hilary Benn, shadow foreign secretary, after he told Corbyn in a phone call that he no longer had confidence in his leadership. Their calls for Corbyn to step aside have so far fallen on deaf ears, however with the Labour leader — who has the support of industrial trade unions — refusing to stand down. Issuing a statement on Twitter, Corbyn said he will stand in any new leadership election and said he had the support of millions of party members and supporters. Tweet As their leader digs in, more resignations came Monday morning and even Corbyn's deputy, Tom Watson, has told his boss to resign. Labour politicians are expected to discuss a motion of no confidence against Corbyn later in the day, meaning that the U.K.'s second main party could also be facing a leadership campaign before long.

Disunited Kingdom

Leaving aside the place of Britain in Europe, the referendum has cast uncertainty upon the future of the U.K. as a whole. Scotland First Minister Nicola Sturgeon announced soon after the result that she would be seeking a second independence referendum and for Scotland to remain a part of the EU after Scots voted overwhelmingly to remain.

In addition, several nationalist politicians in Northern Ireland (where, likewise, the vote was generally to remain a part of the EU) also called for the country to be reunited with the Republic of Ireland. With the existence of the U.K. as a united entity at risk and the political establishment in meltdown, Alastair Campbell, who was director of communications for former Labour Prime Minister Tony Blair, told CNBC on Sunday that the U.K. was in "a pretty dangerous state" following the vote. "I certainly think that we're in a pretty parlous and perilous state right now. The country has taken a monumental decision without a lot of people really being clear about what the consequences might be, a lot of people that voted for it now realizing that they were lied to pretty systematically by those that campaigned," he said. "You've got a government in turmoil with a leadership vacuum, you've got the Labour Party in turmoil with a leadership vacuum and you've got some really unpleasant stuff going on in Britain as well. Lots of racially motivated attacks and some really disgusting stuff here and I think it's really sad."