LONDON — Conservative Party candidates to succeed David Cameron as prime minister started putting themselves forward on Wednesday. The Labor Party was descending further into civil war over whether its leader, Jeremy Corbyn, can keep his job while most Labor legislators want him to quit.

Given the chaos, there is growing talk that the endgame for Britain’s political crisis could be another general election, perhaps as soon as this fall, in an effort to bring some clarity to the nation’s leadership and direction after the vote last week to leave the European Union.

The current Parliament, elected in May 2015, still has nearly four years of its five-year term to run. But once the Conservatives settle on a successor to Cameron, a process that is likely to play out by September, the new prime minister may well want to secure his or her own electoral mandate, especially given the sharp turn Britain has taken and the conflicts over how and whether to proceed with the process of decoupling from Europe.

But even the question of an early general election is proving divisive.

Boris Johnson, the former mayor of London and a leader of the Leave campaign, has been canvassing fellow Conservative members of Parliament, seeking support for his candidacy and getting their views on the advantages of an early general election.

But his main rival, Theresa May, the home secretary, who supported staying in the EU, is considered more of a continuity candidate and may not want to go back to voters so soon, a view shared among those Conservatives who were elected to their seats for the first time 13 months ago.

But it is the prospect of a quick election that has motivated Labor members in Parliament to try to oust their party leader, Corbyn, voting overwhelmingly on Tuesday for a motion of no confidence in him that is a necessary prelude to a leadership contest.

The rebels fear that under Corbyn, 67, a leftist who has repudiated what remained of the centrist New Labor movement of the Tony Blair era, the party will be crushed and they will lose their seats with an even worse showing than in the last general election in May 2015, when the Conservatives won an outright majority.

About three-quarters of Labor’s shadow cabinet, made up of senior legislators who speak on policy for the party, have resigned so far this week, trying to force Corbyn to step down.

Corbyn has refused. He has said he will seek another mandate from the grass-roots members and supporters of Labor, who elected him by a substantial margin in the first place. But it is unclear whether he remains as popular among the rank-and-file after leading a halfhearted campaign to keep Britain in the EU, when many traditional Labor voters chose to stay home or vote against the party’s position.

The outcome of any contest would also depend on whom the more centrist Labor legislators find to run against Corbyn. That may be Angela Eagle, a senior figure of the softer left and the daughter of a printworker, or a more centrist figure like Tom Watson, who was elected deputy leader last year. Other possible contenders include Dan Jarvis and Chuka Umunna, both of whom decided not to run against Corbyn last year, or Yvette Cooper, who did and lost.

Corbyn has “no plan for a looming general election,’’ Cooper said on Tuesday, urging him to resign quickly.

“Jeremy would be letting down Labor voters and communities across the country who badly need a strong Labor voice right now, and who badly need a Labor government, if he drags this out any longer,’’ Cooper said. “I hope he does the right thing in the party and stands down swiftly because we cannot drift and leave’’ the Conservatives “to shape Britain’s future.’’

In Parliament on Wednesday, Cameron got in on the act, calling on Corbyn to quit and attributing to him some of the blame for the outcome of the referendum.

“It might be in my party’s interest for him to sit there,’’ Cameron said. “It’s not in the national interest. And I would say, ‘For heaven’s sake man, go!’ ’’

For the Conservatives, there is at least a clear path toward a new leader, and Johnson and May are clear favorites. But party history suggests that favorites sometimes founder.