The five-week suspension of Parliament will begin later, after MPs are expected to again reject government calls for a snap election.
Opposition MPs confirmed they would not back the push for a 15 October poll, insisting a law blocking a no-deal Brexit must be implemented first.
Ministers have called the law “lousy” and said they would “test to the limit” what it required of them.
Boris Johnson has been warned he could face legal action for flouting it.
At present, UK law states that the country will leave the EU on 31 October, regardless of whether a withdrawal deal has been agreed with Brussels or not.
But the new legislation, which was granted royal assent on Monday, changes that, and will force the PM to seek a delay to 31 January 2020 unless a deal – or a no-deal exit – is approved by MPs by 19 October.
BBC political editor Laura Kuenssberg said although No 10 insisted it was not looking to break the new law, efforts were underway to examine ways of getting around it.
Meanwhile, John Bercow has said he will stand down as Commons Speaker and MP at the next election, or on 31 October, whichever comes first, after 10 years in the role.
Two emergency debates are taking place in the Commons, ahead of a vote on a general election.
MPs have begun debating an application from Dominic Grieve – now sitting as an independent after losing the Tory whip – who is seeking to ensure the publication of government communications relating to the suspension of Parliament.
He is also pressing for full disclosure of all documents relating to Operation Yellowhammer, the government’s no-deal contingency plan, shared with ministers since 23 July.
Later, the second emergency debate on the rule of law and ministers’ obligation to uphold it – proposed by Labour leader Jeremy Corbyn – will take place.
The prorogation – or suspension – of Parliament until 14 October will begin at the end of Monday’s sitting.
It means MPs will not get another chance to vote for an early election until after then, meaning a poll would not be possible until late November at the earliest.
Mr Johnson argues he has been forced into seeking an election because the no-deal delay bill makes further negotiation with the EU pointless – but he needs the support of two-thirds of MPs to hold a snap poll.
Labour, the SNP, the Liberal Democrats, the Green Party, the Independent Group for Change and Plaid Cymru met on Monday morning and agreed not to back the motion for an election.
Mr Corbyn said MPs did not discuss the date of a poll, but the “obvious time” to decide that would be after the EU Council meeting in mid-October as “that’s when the British government will have to have made its application” for an extension.
Downing Street has accused Labour of denying the public the right to have a say and is arguing that Mr Corbyn should take the opportunity to seek his own mandate from the public to delay Brexit.
But the Labour leader said he thought it was “extraordinary” that the prime minister, having “lost every vote he has put to Parliament in the few days” tells the country he will defy Parliament.
Elsewhere, one plan reportedly under discussion to get round the Brexit delay legislation is to ask a sympathetic EU member to veto an extension.
Another potential option would be to formally send the extension request mandated by the new law, but also send a second letter to the EU making it clear the UK government does not want one.
However, Lord Sumption, a former UK Supreme Court judge, said such a ploy would not be legal.
“To send the letter and then try and neutralise it seems to me to be plainly a breach of the act,” he told BBC Radio 4’s Today programme.
Earlier on Monday, Mr Johnson held talks with Leo Varadkar in Dublin – his first meeting with the Irish prime minister since he entered No 10.
The Irish border has proved a key sticking point in attempts to agree on a Brexit deal between the UK and the EU.
Mr Johnson wants the controversial backstop – an insurance policy against a hard border on the island of Ireland – scrapped, because if applied, it would see the UK stay in a single customs territory with the EU and align with current and future EU competition rules.
Northern Ireland would also stay aligned to some rules of the EU single market.
These arrangements would apply unless and until both the EU and UK agreed they were no longer necessary.
The PM told a press conference he believed a deal could be done and an alternative to the backstop found.
Leaving without a deal – something he said again he was willing to do – “would be a failure of statecraft for which we will all be responsible”, Mr Johnson added.
Mr Varadkar said Ireland was “open to alternatives” to the backstop “but they must be realistic”, adding: “We haven’t received such proposals to date.”
He has said he is open to a solution involving a backstop which only applies to Northern Ireland, but Democratic Unionist Party MPs – Mr Johnson’s allies in Parliament – strongly oppose the idea.
Some critics of the prime minister – including Amber Rudd, who resigned as work and pensions secretary at the weekend – have questioned how serious he is about trying to reach a new deal with Brussels.
Ms Rudd told the BBC there was “very little evidence” the government would get a new deal, and when she asked for details of the efforts she received a “one-page summary”.
The story is of a prime minister increasingly hemmed in.
He will almost certainly lose the election vote today, the no-deal bill is set to become law, and he’s lost control of the parliamentary timetable because of his own decision to prorogue.
The easiest way out of this is to get a deal with the EU, but he seems to have closed down the scope for doing that by being so tough on the backstop. There’s also the risk of a mutiny on his backbenches if he comes up with anything that looks remotely like Theresa May’s deal.
That’s why we’ve ended up with this talk about trying to circumvent the law, by sending a second letter after the one requesting a Brexit extension. The idea behind that is to say to the EU, “Look, we’re going to be unhelpful, obstructive, noisy, you should just get rid of us,” in the hope that Brussels will say, ‘”Good point, no extension, we’ll just cut you loose.”
The law, though, may stop the PM from doing that – it may require him to make the case for an extension in good faith.