How Britain’s parties are struggling to make sense of post-Brexit chaos

The political reverberations of Britain's vote to leave the European Union show no signs of fading.

Internal rifts continue to stretch Britain’s biggest political parties at the seams following the vote to leave the European Union. As top party members struggle to wrest some semblance of consensus from the chaos – and install new leaders who can guide them back to calm – the consequences of the exit itself are looming.

The worse-off of the two parties in some respects appears to be Labour, whose top member Jeremy Corbyn rose to the helm just a year ago on the strength of a grass-roots groundswell. At the moment, he seems to hang on by a thread: The party's members, and his own shadow cabinet, have abandoned their tepid acceptance, turning fiercely against what they consider his weak leadership during the doomed campaign to keep Britain in the EU.

Some have also accused him of tolerating anti-Semitism from leftist supporters. On Friday, the flames were further fanned when Mr. Corbyn was thought to have compared Israel to the Islamic State.

Earlier this week, Corbyn lost a no-confidence vote by a large margin, though he vowed to remain.

"I was democratically elected leader of our party for a new kind of politics by 60 percent of Labour members and supporters, and I will not betray them by resigning," he said after the vote, according to The New York Times.

The party seems to have no obviously suitable replacements. A new poll suggests that the crisis of confidence in Corbyn, while widespread, might be more acute among the party's actual power-holders, rather than the rank and file: while a majority of party members say Corbyn should step down before the next election, they also support him over any other candidate for the top position. And though his approval ratings have slipped drastically, a slim majority still approve of his leadership. London has seen thousands of Corbyn's grass-roots fans turn up to demonstrations in support of him.

The Conservatives' ranks are less mutinous. After former London mayor Boris Johnson's stunning announcement that he would drop out of the race for the nomination for prime minister, a handful of establishment candidates have stepped up.

The party's crisis may stem in part from the credibility of its promises: Mr. Johnson led a campaign that achieved the unthinkable, then abandoned the party when it came time to steer Britain through possible calamity. Now, the favorite for the nomination is Home Secretary Theresa May, who sought to preserve Britain's membership in the EU.

Whoever takes the helm will face a European Union possibly tempted to punish Britain for leaving it. "The EU doesn't want to make this easy," said Peter Moloney, a Boston College professor who specializes in the history of the EU, in an interview with CNBC. "They don't want anyone to copy the British, and making the deal attractive is not the way to ensure that the other 27 members stay in line." 

The foremost question in Britain's future extrication from Europe is how it will regulate migration into the United Kindgom. At the first EU meeting since the referendum vote, European leaders said that Britain could not expect to cap migration without having its access to the Europe-wide market fettered, reported The Wall Street Journal. The EU considers the free movement of goods, workers, services, and capital to be its "four freedoms." 

"Those who want to have free access to our internal market," said European Commission President Jean-Claude Juncker, "they have first to implement the four freedoms without exception and I have to add without nuances."