LONDON — Though she admits disliking the social side of politics, Prime Minister Theresa May hosted lawmakers at a party in Downing Street this week, hoping to salvage her much-maligned plans for Britain’s departure from the European Union, or Brexit.

But despite wine, canapés and what one guest called a “very pleasant social occasion,” Mrs. May brings her deal to Parliament on Wednesday knowing that she faces virtually certain defeat in a vote next week — one that could mean weeks of perilous political brinkmanship for Britain.

Mrs. May postponed the vote last month, calculating that she would lose, yet has little to show for the delay. More than two and a half years after Britons opted to leave the European Union, a divided country is still wrestling with the implications of that referendum decision and, as ever with Brexit, the answers seem to lie just over the horizon.

“We won’t get to the endgame until one or other of the options for Brexit are eliminated,” said Charles Grant, director of the Center of European Reform, a research institute, “and maybe not until March.”