BRUSSELS — With less than 48 hours before Britain’s scheduled departure, the European Union extended the exit deadline early Thursday until the end of October, avoiding a devastating cliff-edge divorce but settling none of the issues that have plunged British politics into chaos, dysfunction and recrimination.

On another difficult night for Prime Minister Theresa May of Britain, European leaders scrapped her proposal for a postponement until June 30, concluding that such a short deadline was unrealistic for the departure known as Brexit. They agreed, however, to review the arrangement at the end of June to prevent British disruption to the bloc while the nation remains in Europe’s departure lounge.

Although the intense pressure of recent weeks may abate for now, the path ahead still resembles a minefield, dotted with explosive issues like a possible attempt to topple Mrs. May, a general election or a second Brexit referendum — or some combination of the three. Most immediately, Mrs. May is likely to face calls to step down, and potential successors are already trying to raise money and advertise their credentials.

At a news conference, Donald Tusk, the president of the European Council, said that the two sides had agreed to what he called “a flexible extension” until Oct. 31, adding that this provided an “additional six months for the U.K. to find the best possible solution.” In essence, the bloc agreed to kick the Brexit can down the road for another six months.