It is the job of “everybody in Parliament” to deliver Brexit, Prime Minister Boris Johnson has said at the end of the G7 summit in France.
Mr Johnson’s comments come as MPs from other parties prepare to meet to discuss ways to avoid the UK leaving the EU without a deal on 31 October.
The PM added that EU leaders also now just want Brexit to be “over”.
No 10 earlier said the EU should not listen to the “very wrong messages” from MPs who want to stop Brexit.
A senior British official said the PM had been clear to European leaders at the summit that the idea Brexit will be stopped was “incorrect”.
Talks between UK MPs on how to avoid no deal are planned for Tuesday.
But Mr Johnson has repeatedly insisted that the UK will leave the EU on 31 October, with or without a deal.
Labour leader Jeremy Corbyn wants to call a vote of no confidence in the government to prevent a no-deal Brexit.
If he were to win a vote, Mr Corbyn plans to become a caretaker prime minister, delay Brexit, call a snap election and campaign for another referendum.
However, his plan, to be discussed by MPs from different political parties on Tuesday, has met with resistance from some key potential allies – including the pro-EU Liberal Democrats.
At the G7 summit, the Downing Street spokesperson said: “We are leaving on October 31 with a deal or without.
“The prime minister would prefer it to be a deal but we will be leaving on October 31 and he is very clear about that.
“He thinks European leaders should not be listening to the very wrong messages emerging from some parliamentarians who think that they will stop Brexit.”
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The official said Mr Johnson has been “repeatedly clear that parliamentarians and politicians don’t get to choose which public votes they respect”.
If a new Brexit deal was negotiated, the public would “expect Parliament to find a way” to pass the necessary laws to allow the UK to leave at the end of October, the official added.
On Sunday, Mr Johnson told the BBC the chances of securing a new Brexit deal were “touch and go”, after having previously said the odds of no deal were “a million to one”.
He also said if there is no deal, the UK would keep a “very substantial” part of the £39bn former prime minister Theresa May had agreed to pay the EU in her withdrawal agreement – the deal which British MPs rejected three times.
But, responding on Monday, European Commission spokeswoman Mina Andreeva said the UK must honour commitments made during its EU membership, and said this was “especially true in a no-deal scenario”.
She said that “settling accounts is essential to starting off a new relationship on the right foot”.
Guy Verhofstadt, the European Parliament’s Brexit co-ordinator, said: “If the UK doesn’t pay what is due, the EU will not negotiate a trade deal.”
The G7 summit – a get-together of most of the leaders of the world’s largest economies – comes with just over two months until the UK is scheduled to leave the EU.
The SNP, Liberal Democrats, Change UK, Plaid Cymru and the Green Party have all accepted the invitation to meet Mr Corbyn to discuss his proposals to avert a no-deal Brexit on Tuesday.
But Ms Swinson said Mr Corbyn’s plans risks jeopardising a potential vote of no confidence in the government.
She said the discussions should examine how to seize control of Commons business, oust Mr Johnson and install an emergency “government of national unity”.
The Labour leader’s insistence on being interim leader meant there was a danger not enough MPs would support the vote, Ms Swinson said.
In a letter to Mr Corbyn, she said: “As you have said that you would do anything to avoid no deal, I hope you are open to a discussion about how conceding this point may open the door to a no-confidence vote succeeding. Its success must be the priority.”
Labour has not responded to the letter, but has instead referred to comments made by its shadow international trade secretary, Barry Gardiner, who on Sunday described Ms Swinson as “extremely petulant” for dismissing Mr Corbyn’s initial proposal.
Mr Corbyn has said he would call a no-confidence vote at the “earliest opportunity when we can be confident of success”. That cannot happen before 3 September, when MPs return from summer recess.
In order for such a vote to succeed, Labour would require support from across the House of Commons, including the Lib Dems, the SNP and Conservative rebels.
Brexit: The job of all MPs is to deliver UK’s exit from EU – Johnson}