The House of Lords has agreed to progress a backbench bill seeking to block a no-deal Brexit, as Boris Johnson prepared to make a speech calling again for Labour to allow a general election.

At about 1.30am on Thursday, following hours of debate, peers were told that the cross-party bill, tabled by Labour’s Hilary Benn, would be returned to the lower house by 5pm on Friday, ruling out the prospect of fresh attempts at a filibuster.

It could then be voted on again by MPs on Monday and presented for royal assent, the Lords heard. Peers are due to debate the Benn bill itself and amendments on Thursday.

The bill had already been passed by the Commons with the assistance of rebel Tories, after they helped to seize control of the parliamentary agenda to rush the measure through. Johnson responded to the backbench efforts on Wednesday by seeking a snap election under the Fixed-term Parliaments Act. However, opposition parties abstained or opposed the vote, denying the PM the necessary two-thirds majority – and meaning he has lost every Commons vote so far.

Johnson was scheduled to make a speech in an as-yet undisclosed location later on Thursday, and take questions from the media. A spokesman for No 10 said the prime minister would “speak directly to the public, setting out the vital choice that faces our country”.

He added that Johnson would refuse to abide by the Benn bill, which would mandate him to seek an extension to Brexit until at least 31 January if, by the end of next month’s crucial European council summit, he has not secured a deal or gained MPs’ consent for no deal.

“The PM will not do this,” he said. “It is clear the only action is to go back to the people and give them the opportunity to decide what they want: Boris to go to Brussels and get a deal, or leave without one on 31 October.”

The other alternative, the spokesman said, was Corbyn taking over the negotiations, “begging for more delay, more dither and accepting whatever terms Brussels imposes over our nation”.

Labour has said it will back an election after the no-deal blocking bill becomes law, which would guarantee that Johnson could not force no-deal on 31 October. However, the party remains undecided whether it would back Johnson’s choice of a 15 October polling day, or want to wait.

After the marathon Lords session, Lady Smith, Labour’s leader in the upper house, said she hoped that there would be “no further frustrations” of the bill on Friday.

“It has been quite a night. It has been a long debate – and I am grateful to the noble lords who have stayed the course – it shows the importance of the work we do but also the issue on which we are debating,” she said. “I am grateful that we are now able to confirm that we will be able to complete all stages of the bill in a time-honoured way by 5pm Friday.”

Richard Newby, the leader of the Liberal Democrats in the Lords, told the chamber he was very pleased that he would no longer need to use a duvet he had brought to parliament: “I don’t think that carrying on through 24 or 48 hours as we have been doing in a sort of pathetic attempt to set a new Guinness world record … would do anybody any favours.”

Andrew Adonis (@Andrew_Adonis) Government chief whip announces government cave-in at 1.20 am - they are lifting the filibuster after 10 hours, with a commitment that the EU Bill will pass by 5pm Friday. We have stopped no deal - & we can now go home 🆒😊😍🇪🇺

LabourLordsUK (@LabourLordsUK) #WhiteSmoke...



Govt commits to allowing #BennBill to complete all stages in course of Thurs & Friday - with the bill then going back to the Commons for any further consideration on Monday@LadyBasildon confirms that fresh business motion in her name will appear on Thurs am

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There had been fears that the bill would be stalled in the Lords, with the Labour peer and leading lawyer Lady Kennedy of The Shaws accusing the Tory peer Lord True, who submitted a raft of amendments, of time-wasting.