Brexit deal vote likely in early June; Brexit rebels to vote against Ms. May’s deal; “What has changed,” asks the Northern Irish Democratic Unionist Party, which props up Ms. May’s minority government; Labour worries that Ms. May’s successor could renege

Brexit-supporting rebels in British Prime Minister Theresa May’s party said on May 15 they would vote down her European Union divorce deal when she brings it back to parliament early next month.

Brexit had been due to take place on March 29 but lawmakers rejected the withdrawal agreement that Ms. May struck with Brussels three times. The United Kingdom is now scheduled to leave the EU by October 31.

Ms. May will bring a Withdrawal Agreement Bill, which implements the departure terms, in the week beginning June 3 — the same date that U.S. President Donald Trump begins a state visit to Britain at the invitation of Queen Elizabeth.

Brexit supporters in Ms. May’s divided Conservative party said her deal was as dead as her crisis-riven three-year premiership.

“I have talked to colleagues, some of whom voted for it last time, and they think it is dead and they will vote against it this time,” Peter Bone, a Conservative lawmaker and a prominent supporter of leaving the EU, told Talk Radio. “I know they wouldn’t vote for it. It seems absurd to bring it back. It is the same thing again, again and again.”

Ms. May, who secured the Conservative Party leadership and the premiership in the chaos that followed the 2016 Brexit referendum, is already under pressure from some of her own lawmakers to set a date for her departure.

Defeat in the June vote would likely spell the end of her divorce deal and her premiership.

Brexit supporters fear that Ms. May’s deal will keep the United Kingdom trapped within the EU’s orbit for years and that it could ultimately pull the British province of Northern Ireland towards the bloc.

‘What has changed?’

Nearly three years after the United Kingdom voted 52% to 48% to leave the EU, politicians still disagree about when, how or even if the divorce will take place.

Before her deal was defeated the last time, 344-286 on March 29, Ms. May had promised to resign if it was passed. It was voted down first in January and again in mid-March.

A constant sticking point has been the Irish backstop, an insurance policy aimed at avoiding post-Brexit controls on the border between Northern Ireland and EU state Ireland.

“If the Prime Minister brings the Withdrawal bill to the Commons for a vote the question will be ‘what has changed,’” asked Nigel Dodds, parliamentary leader of the Northern Irish Democratic Unionist Party (DUP), which props up Ms. May’s minority government. “Unless she can demonstrate something new that addresses the problem of the backstop then it is highly likely her deal will go down to defeat once again,” Mr. Dodds said.

A majority of members of the European Research Group, a large Brexit-supporting faction in the Conservative Party, will vote against Ms. May’s deal, said Owen Paterson, a former Minister. “Sadly, we will vote against it again,” he said, adding that it could divide the country.

As positions harden in parliament, with many wanting to either leave the EU without a deal or to stop Brexit altogether, Ms. May has turned to the Opposition Labour Party, led by veteran socialist Jeremy Corbyn, to negotiate a way out of the impasse.

But after more than four weeks of talks, the two party leaders appear no closer to agreeing a common position.

“We haven’t seen the significant shift yet that we require to be able to support a deal,” Labour’s second most powerful man, finance chief John McDonnell, said on May 14. “We are not near what we want.”

Mr. McDonnell said he was deeply concerned a future Conservative leader could renege on any promises made by the current government.