The leader of Britain's opposition Labour party, Jeremy Corbyn, leaves his home in London on Tuesday. (Neil Hall/Reuters)

The political implosion at the top of British politics that followed last week’s referendum widened further on Tuesday, rendering both the country’s main parties effectively leaderless at a time when the U.K. is under pressure to make fundamental decisions about its new place in the world.

The turbulence wrought by the public’s decision to exit the European Union had already claimed the career of Prime Minister David Cameron, leaving the governing Conservative Party to joust through the summer over who will lead the country starting in September.

Now it has also paralyzed the opposition Labour Party, with an overwhelming majority of party leader Jeremy Corbyn’s parliamentary members voting on Tuesday to oust him. Rather than step down, Corbyn vowed to fight on – triggering what will likely be an ugly and protracted war for the party’s soul.

The dysfunction atop both parties – which together have led Britain through war, peace, austerity and prosperity for the past century – leaves the country with a gaping leadership void as it attempts to navigate the biggest transformation of its global role since it shed its empire.

“The pressures on the British political system are absolutely extraordinary at the moment,” said Tony Travers, a political scientist at the London School of Economics. “The British political system, as much as any, relies on the idea of a powerful government and a powerful and acceptable opposition. Right now, neither of those are in place.”

The vacuum was evident in Brussels Tuesday as a chastened Cameron met the 27 fellow European leaders whose union his people so dramatically spurned last week. Cameron, however, was unable to speak up for his nation’s plans post-Brexit, as the divorce between the U.K. and the E.U. is known. Instead, he said, that will be left to his successor.

With Cameron rendered a mere caretaker, the real authority in Britain is now believed to rest with the leaders who championed the case for “leave.”

But as has been true since last Thursday’s vote, the leaders of the pro-Brexit campaign were conspicuously silent, avoiding the media and doing little to clarify their plans for how the country will conduct the messy business of extricating itself from decades of membership in the E.U. and its precursors.

In their limited public statements since the vote, some of the most prominent “leave” backers have seemed to walk back their promises that Britain post-Brexit will enjoy all the benefits of E.U. membership without the burdens. European leaders made clear Tuesday that position is untenable, while pushing Britain to launch negotiations as soon as possible.

With its politics in disarray, Britain wants to avoid starting talks until it has a new prime minister in place – a process that will not be complete until Sept. 9.

The new prime minister will not be chosen by the public. Instead, he or she will be picked through a two-stage process, with Tory members of Parliament first whittling the field of candidates down to two and then the party’s rank and file choosing a winner.

Boris Johnson, the former mayor of London who led the leave campaign, is considered the favorite for the job. But he has not declared his intentions, and there are already indications he could face a more serious challenge than was previously thought.

“This is going to be Boris versus ‘stop Boris,’” Travers said.

A number of candidates were already wading in on Tuesday, with the field expected to be set by Thursday, when nominations close. Among those who have said they are likely to run are health secretary Jeremy Hunt, former defense secretary Liam Fox and work and pensions secretary Stephen Crabb.

Also expected to jump in is Theresa May, who handles the country’s domestic security as the minister of home affairs.

May endorsed “remain” during the referendum campaign, saying that she believed Britain was safer within the European Union. But she was nearly invisible on the campaign trail, and she has long held Euroskeptic views. Some within the party have suggested she could be a compromise candidate who would bridge the warring factions.

A poll published in the Times of London newspaper on Tuesday suggested that Johnson could actually lose among the Tory rank and file in a match-up with May.

The man expected to be Cameron’s chosen successor, chancellor of the exchequer George Osborne, ruled himself out of the leadership contest Tuesday. He told the BBC that he could not unite the party and that he continues to believe Brexit would make the country “poorer.”

As the Tories prepared for what is likely to be a contentious leadership fight, Labour on Tuesday fell into civil war after balloting revealed that 172 members of the party’s Parliamentary delegation have no confidence in Corbyn, their leader. Just 40 backed him.

Tuesday’s vote is nonbinding, and Corbyn — a north London politician whose views have been compared to those of Sen. Bernie Sanders of Vermont — was defiant after the vote, pledging not to step down.

“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 wrote in a statement released within minutes of the result being revealed. "Today’s vote by [members of Parliament] has no constitutional legitimacy."

But the vote is likely to lead to a new leadership contest that could deepen divisions within a party already riven with fractures among its moderate, soft left and hard-left factions. The British press widely reported Tuesday evening that Angela Eagle, a former Corbyn lieutenant, is the most likely candidate to take him on.

Corbyn has suggested he will run again in any leadership contest— and he could well win, given his popularity with the rank and file.

But Tuesday's vote shows unequivocally that his own colleagues in Parliament want him gone.

Corbyn’s detractors in Labour blame him for a lackluster campaign to keep Britain in the E.U. Although Labour officially supported the “remain” camp, Corbyn was a fleeting presence on the campaign trail, and polls showed that many Labour members were not aware of their party’s official position.

Corbyn had long been a fierce critic of the E.U., arguing it had become a tool of corporations and other vested interests.

A former member of Corbyn’s shadow cabinet, Chris Bryant, told the BBC on Monday that he believed the Labour leader may have actually voted to leave in the privacy of the voting booth. Corbyn’s backers have disputed that.

Corbyn’s predicament comes only nine months after his improbable emergence from the far-left fringe to take ownership of a party that last governed under the more centrist Tony Blair and Gordon Brown.

Critics worry that Corbyn could lead the party to an electoral wipeout if the Conservatives call a new election before year’s end. Although no new vote is planned until 2020, some are now advocating for a fresh vote once the Tories have chosen their new leader.

“I am very concerned that Jeremy Corbyn has no plan to reunite the Labour movement, no plan to respond to the deep and serious issues the referendum has thrown up, and no plan for a looming general election,” said senior Labour politician Yvette Cooper, who lost to Corbyn in last year’s leadership contest.

Even as politicians wrestled at Westminster, thousands of pro-E.U. demonstrators turned out in central London to call for a re-run of last Thursday’s vote. They unfurled E.U. flags and chanted “E.U. we love you!”

Such displays of affection were almost completely absent from the referendum campaign. But demonstrators said people only now realize what’s at stake.

“I don’t think people understood what it meant,” said Kym Nagyos, a 28-year-old French make-up artist who has lived in Britain for 9 years. “You can tell the ‘leavers’ didn't think of the consequences. They don't have a plan."

Karla Adam contributed to this report.