People walk over Westminster Bridge in London wrapped in British flags on Sunday. (Odd Andersen/AFP/Getty Images)

Britain on Monday accelerated its possible date with destiny outside the European Union, bringing forward the selection of its new prime minister by a month in a move that may help assuage European demands for a more rapid withdrawal.

By picking a new leader in September rather than October, the country could be free to move faster with its departure from the 28-member club. Outgoing Prime Minister David Cameron insisted on Monday that the country will delay the triggering of exit talks — a point from which there will be no turning back — until his successor is in place.

The move came as markets tumbled worldwide, the pound hit a 31-year low and a respected financial agency cut Britain’s credit rating. Amid the growing tumult, President François Hollande of France said his country’s island neighbor needs to get out quickly to end the uncertainty.

“We must not lose time, neither for dealing in a suitable way with the question of the United Kingdom’s exit, nor for providing a new impetus for the E.U.,” Hollande said in a news conference alongside his German and Italian counterparts.

But Britain is hardly prepared for talks to begin, with its politics in chaos, its currency reeling and its leadership in question. Since the British public voted to leave the E.U. on Thursday, the top advocates for an exit have been nearly invisible, and Cameron has deferred to his as-yet-unknown successor all the critical questions of how an exit will play out.

The ambiguity has unsettled investors and will likely make for awkward exchanges when Cameron travels to Brussels on Tuesday to meet the 27 other E.U. leaders whose organization has just been spurned by Cameron’s voters.

In the first session of Parliament since Thursday’s historic vote, Cameron said Monday that his country alone will set the timetable to launch the talks for the split.

“This is our sovereign decision,” Cameron said in an appearance in the House of Commons that was met with rapturous applause. “It will be for Britain and Britain alone to take.”

Cameron was adamant, however, that Britain will leave: Despite campaigning relentlessly for a vote to “remain,” the prime minister said the will of the public “must be accepted.”

He also seemed to dash the hopes — however faint — of the millions of Britons who have signed a petition in recent days pushing for a rerun of the referendum in the expectation that the 52 percent to 48 percent “leave” victory will be reversed.

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“I’m not planning a second referendum,” Cameron said.

Cameron’s early September departure date, set on Monday by a committee that decides the rules for picking a new prime minister, is a month earlier than he had stated when he announced his resignation plans Friday.

The new date might suggest a concession to European leaders who have been pushing for Britain to move more quickly to invoke Article 50 of the Lisbon Treaty — the mechanism by which countries can leave the European Union.

It is not clear how much leverage Europe has to push Britain into an even earlier exit. But European leaders — particularly the French — have not been shy in arguing for a fast breakup in order to end the uncertainty. Financial policymakers and others worry that dragging out the British break could accentuate the turbulence that has already taken a toll on global markets.

As the pound fell further Monday, and European stock markets and Wall Street traded sharply downward, London’s main FTSE-100 share index closed down nearly 2.6 percent.

After markets closed in London on Monday, the Standard & Poor’s Global Ratings agency stripped Britain of its triple-A rating — a humiliating blow for the country and one that could cost its economy.

With the unity of the E.U.’s 27 other members on the line, top European leaders have taken a tough line with Britain.

German Chancellor Angela Merkel on Monday ruled out the chance of “informal talks” that could lay the groundwork for a deal before Britain officially pulls the Article 50 lever.

Merkel, however, appeared somewhat more patient than Hollande. Asked about a timeline, she acknowledged that it appeared to have been accelerated on Monday with Cameron’s Conservative Party moving up its selection of the new prime minister. She said E.U. members would discuss the matter with Cameron, but would approach the discussion “calmly.”

“I can’t comment on how long it will take,” she said. “I can only repeat what I said: ‘as little waiting as possible.’ ”

With Germany taking a seemingly more nuanced tack than the hard-line French, some German officials even appeared to hold out hope that Britain might not leave after all.

Jürgen Hardt, foreign policy spokesman in the German Parliament for the ruling coalition and a close Merkel ally, suggested Berlin would be willing to give London more time if there were clear indications that British politicians were moving to find a way to remain in the E.U. despite the vote.

“There is only one reason why the British government should ask for more time. This would be that it is reconsidering the decision to leave the E.U.,” Hardt said.

Britain’s political system, as well as its economy, have been thrown into turmoil by the outcome of the referendum, which was not expected by the markets, analysts or perhaps even the politicians who campaigned for a departure.

Both of Britain’s main parties — Conservative and Labour — are now effectively engaged in civil wars, with the soul of both up for grabs.

Labour leader Jeremy Corbyn faced an onslaught of defections from his senior ranks on Monday, and is expected to lose a vote of confidence on Tuesday — triggering a fresh leadership contest less than a year after the hard-liner first won control of the party.

The Conservative leadership struggle, meanwhile, will determine who succeeds Cameron as prime minister.

Leading Brexit advocate Boris Johnson, the former mayor of London, is considered the favorite. But he has said little about his plan for the country post-Brexit, has not submitted to detailed questioning from the media since Thursday and was not present for Cameron’s appearance in the House of Commons on Monday.

Johnson wrote an op-ed in Monday’s Daily Telegraph that seemed to walk back promises that a non-E.U. Britain would be able to dramatically limit immigration, which was a core voter concern.

“It is said that those who voted Leave were mainly driven by anxieties about immigration,” he wrote. “I do not believe that is so.”

Johnson also suggested he is in no hurry for Britain to start negotiations to leave the bloc, despite campaigning for months for an exit from what he depicted as a tyrannical Brussels bureaucracy that rode roughshod over British democracy.

In Brussels, a senior E.U. official said there was little expectation that Britain would give formal notice of its departure in the immediate future, given the scale of the political crisis.

“There is a broad understanding why it is not possible, why it will not take place on Tuesday,” said the official, speaking on the condition of anonymity to brief reporters ahead of Tuesday’s summit. “Everyone recognizes that right now there is quite a significant crisis in the U.K.”

Secretary of State John F. Kerry was among those appealing for calm Monday and counseling against any move to push Britain into a hasty decision.

“It is absolutely essential that we stay focused on how in this transitional period, nobody loses their head, nobody goes off half-cocked, people don’t start ginning up scatterbrained or revengeful premises,” Kerry said in Brussels before heading to London for further crisis talks with Cameron and British Foreign Secretary Philip Hammond.

Instead, Kerry said, it was time to “look for ways to maintain the strength that will serve the interest and the values that brought us together in the first place.”

Faiola reported from Berlin. Michael Birnbaum in Brussels and Carol Morello in Washington contributed to this report.