The vote on legislation to leave the bloc, known as the Withdrawal Agreement Bill, is scheduled for the week beginning June 3. It is likely to be the final significant act of Mrs. May’s tenure, as she has promised to set a date for her departure after the decision, ending almost three troubled years in power.

Mrs. May’s latest Brexit deal differs from her previous one in that it offers Labour lawmakers more assurances on European standards on workplace protections and environmental rights.

She would also allow Parliament the right to demand, at least temporarily, a type of customs union with the bloc that is designed to prevent tariffs and many border checks on industrial goods, but only until the next general election, scheduled for 2022. And she is also offering the opportunity to vote on the second referendum.

For Conservative Brexit supporters the bill has some sweeteners in that it commits the government to working on technical measures to track goods that would prevent the need for border checks at the Irish border.

Critically, however, this would not guarantee Britain staying out of the so-called Irish backstop, a device to avoid a hard border with Ireland. The backstop would keep the whole of the United Kingdom tied to Europe’s customs rules indefinitely, outraging Brexit supporters who say it defeats the whole purpose of Brexit.

On Tuesday there was a backlash from hard-line pro-Brexit Conservative lawmakers, including Iain Duncan Smith, a former party leader.

“The backstop is still there, it’s a customs union in all but name and it puts Brussels firmly in control of our destiny,” he said in a statement, adding that there was “nothing new or bold about this bad buffet of non-Brexit options,”