But with British Prime Minister David Cameron stepping down on Thursday NZT, his successor will come under pressure from all sides to initiate the split.
Other European leaders want to minimise the uncertainty of British limbo on their economies. In Britain, some hard-line Leave supporters also feared that a step-by-step move towards the EU exit could open room to challenge the decision.
"There should be no decision to invoke Article 50 until the British negotiating strategy is agreed and clear, which means Article 50 should not be invoked before the end of this year," May said when she announced her candidacy for the leadership position shortly after last month's referendum. That could prove to be a difficult position to maintain.
May was a reluctant campaigner for the Remain camp, but she has repeatedly said that the country cannot ignore the referendum decision. "Brexit means Brexit," she said, shortly before Leadsom folded her candidacy.
The prospect of a drawn-out British exit initially sparked fury from European leaders who fear flatlined economies, as businesses and investors wait to see the outcome of the split before making big decisions about where to put their money.
As groups on the continent that are critical of the EU's reach have been encouraged by the British vote, leaders in France and Germany, which both hold elections next year, want to deliver clear messages about the pain of a European pullout and the desirability of staying in.
German Finance Minister Wolfgang Schäuble pointed the finger at Britain last week, saying the referendum "brought so much unrest to the EU" and the rest of the bloc "must do everything possible to limit the damage".
"Europe would be a laughingstock if, after such a decision, it were to say that you have as much time to think it over as you wish," he added.
He said that market pressure could increase the longer the negotiations drag on.
If the timetable is indeed accelerated, the big winners could be those who advocate a more decisive split between Britain and the 27 other EU partners, analysts say.
Britain appears ill-prepared to conduct the complex trade negotiations with the European Union, in part because it ceded that function to the EU. when it joined in 1973. The entire British government has just 20 active trade negotiators, compared with the EU's army of more than 600 trade specialists, a former senior British Foreign Office official, Simon Fraser, said last month.
ABOUT THE BREXIT TRIGGER
1 Once the two-year clock on the talks is triggered, those in the EU who want to drive a hard deal have time on their side
2 After two years, Britain will be out of the EU even if no deal has been reached
3 Tariffs would be adjusted according to World Trade Organisation rules
4 That could devastate Britain's finance and service-based economy.
In Britain and on the continent, those who advocated Britain remaining in the European Union had also hoped that the slower calendar might provide a window that would make clearer the economic pain of withdrawing.
That could have fed support for tighter ties between Britain and the European Union, perhaps like Norway's deal, where the non-EU member nation participates in the common market in exchange for following most EU rules.
"The more time you have to let the bad news sink in, the better chance you have to backpedal on this at least a bit," said Jan Techau, the head of Carnegie Europe, the Brussels outpost of the Washington-based think-tank.
But Europe, too, could benefit from more time to arrive at a common position towards Britain, Techau said.
Right now, countries are split between those that favour a fuller, more drastic break-up and those that believe a closer relationship could benefit both sides.
Ultimately, the shifting schedule may only serve to accelerate the inevitable: a painful severing of ties across the English Channel, one analyst said.
"Two months here or there is irrelevant. What matters is the substance," said Charles Grant, the director of the Centre for European Reform, a London-based policy organisation that advocated staying in the European Union.
"A lot of big businesses don't realise how hard it's going to be. We're going to get screwed badly."
