His supporters ended a night-long filibuster in the upper House of Lords when the government gave up trying to block a measure designed to stop a no-deal Brexit by forcing Johnson to seek a delay if he fails to reach an agreement with Brussels.
The opposition said they should now be able to pass the bill - which he has branded a "surrender document" - before he suspends parliament for over a month next week.
"Govt commits to allowing (the draft legislation) to complete all stages in course of Thursday & Friday - with the bill then going back to the Commons for any further consideration on Monday," the main opposition Labour Party tweeted in the early hours of Thursday morning.
Boris Johnson calls vote on holding early elections after Brexit defeat
The lower House of Commons fast-tracked the legislation on Wednesday and then blocked Johnson's call for an early election that he wants to be held on October 15.
Labour said it will only back the snap poll once it makes sure Johnson is unable to follow through on his threat to take Britain out of the EU with no deal by the October 31 Brexit deadline .
Parliament has now dealt Johnson a rapid series of stinging defeats that have left him a weakened leader just six weeks into his term.
The splintered country still stands no closer to finding out how or when - or even if - it will leave the EU more than three years after the original Brexit vote.
Johnson will also face another legal challenge on Thursday against his decision to order the suspension of parliament from next week until October 14 - a move that his critics have called a "coup" and a "constitutional outrage".
It set the stage for the current furore in Westminster that Johnson tried to stamp out by expelling 21 of its own MPs for voting with the opposition.
They included former finance minister Philip Hammond and grandee Ken Clarke - the longest-serving MP - along with Winston Churchill's grandson Nicholas Soames.
Johnson himself will be on a campaign footing on Thursday as he launches a national effort to recruit 20,000 police officers in Yorkshire in northern England.
The prime minister will also on Thursday host Israeli Prime Minister Benjamin Netanyahu and US Vice President Mike Pence.
He received an endorsement on Wednesday from US President Donald Trump - a key international supporter.
"Boris knows how to win. Don't worry about him. He's going to be ok," Trump told reporters.
Key dates in Britain's Brexit crisis
Johnson has said he wants to strike a deal with EU leaders to allow for an orderly withdrawal from the bloc at the end of next month after 46 years of membership.
But the EU says it has not received any credible proposals from Britain and a senior EU source on Wednesday poured cold water on the idea that a deal could be struck at a summit in Brussels on October 17-18.
Leaked government assessments say a no-deal Brexit could lead to food and fuel shortages and disrupt vital drug supplies.
The food and automotive sectors are particularly concerned about high tariffs for their exports to the EU.
But the government says it will be ready for Brexit when the time comes and has stepped up no-deal preparations.
The law approved by MPs and being debated in the House of Lords, would force the government to request a three-month delay to Brexit if it has not reached a deal by October 19 - two days after an EU summit.
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