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 say they will “test to the limit” what it requires 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, due to get royal assent later, 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 under way to examine ways of getting around it.
Two applications have been made to hold emergency debates in Parliament later.
Labour leader Jeremy Corbyn has requested a debate around the rule of law.
The second application is being made by Dominic Grieve – who lost the Conservative whip last week for voting to block a no-deal Brexit – but it is not clear what the subject will be.
Downing Street confirmed that the expected prorogation – or suspension – of Parliament until 14 October would 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.
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 judge of the UK’s Supreme Court, 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.
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 the election motion, which requires the support of two-thirds of MPs, was defeated last week and is expected to fail again.
Downing Street has accused Labour of denying the public the right to have a say and is arguing that Jeremy Corbyn should take the opportunity to seek his own mandate from the public to delay Brexit.
But the Labour leader told reporters earlier: “I think it is extraordinary that we have a prime minister who has lost every vote he has put to Parliament in the few days it has been back that now goes around the country saying that he is now going to defy Parliament.
“Democracy requires that elected governments are responsible to Parliament itself and the prime minister seems not to be prepared to do that.”
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 a general election.
Mr Corbyn said MPs did not discuss the date of a general election, 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.
Plaid Cymru’s Westminster leader Liz Saville-Roberts said the opposition parties were “united in our belief” that the PM was trying to undermine the new law to block a no-deal Brexit by trying to call an election and he “must be stopped”.
The SNP’s Westminster leader, Ian Blackford, added: “If Boris Johnson wants an election he must obey the law and take a no-deal Brexit off the table.
“It is beyond belief that the prime minister is disrespecting democracy by seeking to shut down Parliament and railroad through an extreme Brexit against the will of Parliament and the people.”
‘Failure of statecraft’
Meanwhile, Boris Johnson has 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 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.
Speaking at a press conference, the PM said 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.”
The Irish prime minister has said he is open to a solution involving a backstop which only applies to Northern Ireland.
But the Democratic Unionist Party – Mr Johnson’s allies in Parliament – strongly opposes the idea.
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 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.
Some critics of the prime minister have questioned how serious he is about trying to reach a new deal with Brussels.
Amber Rudd, who resigned as work and pensions secretary at the weekend, said the government was spending 80-90% of its time on no-deal planning rather than trying to reach an agreement with the EU.
She told the BBC there was “very little evidence” the government would get a new Brexit deal, and when she asked for details of the efforts she received a “one-page summary”.
And she criticised the government for removing the whip from 21 Conservative rebels who voted in favour of the bill to block a no-deal Brexit.
Tory MP and chair of the pro-Brexit European Research Group, Steve Baker, said he was “highly queasy” that party colleagues had lost the whip, but he said they had been warned of the consequences of voting for the bill.
Appearing on BBC Two’s Politics Live, he said he was “absolutely clear” that the government would uphold the law when it came to the bill as well, though he advised them to “look extremely carefully at what the law actually requires”.
And he criticised Labour for not voting in favour of an election, telling the programme: “The government has currently lost control of the House of Commons and that is perfectly plain for anyone to see.
“The proper constitutional thing to do in such circumstances is have a general election and let the public restore the balance in Parliament, but of course Labour won’t do it and that’s why most of this mess is taking place.”