Amber Rudd has admitted “anything could happen” if Theresa May’s Brexit deal is defeated and suggested MPs will then prefer a Final Say referendum to crashing out of the EU.

The new work and pensions secretary undermined the prime minister’s threat of “my deal or no deal”, saying: “There isn’t a majority in the House of Commons to allow that to take place.

Asked if the choice would be a fresh Brexit referendum or leaving with no deal, she replied: “It’s my view that the Commons will stop no deal”.

And she said, of next month’s crucial vote: “If it doesn’t get through, anything could happen. The Brexiteers may lose their Brexit.”

Ms Rudd also cast doubt on Ms May’s plans to seal the Brexit deal at a summit with EU leaders on Sunday, acknowledging there are still obstacles in the way.

“Hopefully it will get through this week,” she said, adding: “There is still a negotiation going on in terms of actually getting this agreement through.”

The comments make Ms Rudd the first cabinet minister to rule out a no-deal Brexit – and the first to suggest an agreement at European level could yet be derailed.

They came as the prime minister prepared to head to Brussels for talks with Jean-Claude Juncker, the head of the European Commission, under huge pressure for further “wins” in the final text.

A historic moment: thousands march to demand Final Say on Brexit Show all 65 1 /65 A historic moment: thousands march to demand Final Say on Brexit A historic moment: thousands march to demand Final Say on Brexit An estimated 700,000 people marched through London to demand a final say on the withdrawal agreement Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Red smoke from a canister hangs in the air as around 100,000 demonstrators march through London during a People's Vote anti-brexit demonstration savings banners and placards Anti-Brexit People's Vote March for the Future in London Rex A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Mayor of London Sadiq Khan takes part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Protesters wearing final Say shirts and holding placards Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit MP Chuka Umunna (left) and MP Vince Cable (right) as MP Anna Soubry (centre) addresses Anti-Brexit campaigners at a rally after the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit A People’s Vote march attendee calls for a Final Say Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Demonstrators with banners 'We're with EU' during the People's Vote March for the Future in London, Britain, 20 October 2018. Reports state that the 'March for the Future' is to be led by a column of young people and call for a Peopleâ€™s Vote on the Brexit deal. After marching through central London, there will be a rally on stage in Parliament Square, including speeches from Mayor of London Sadiq Khan. EPA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Protesters at London’s march for the future in October The Independent A historic moment: thousands march to demand Final Say on Brexit Editor of The Independent Christian Broughton speaks to demonstrators in Parliament Sqaure after they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit A poster at the March for the Future in October The Independent A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Demonstrators hold placards as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final say Brexit march - final say on our furture London, 20 October 2018 Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 campaigner wrapped in EU flag Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say march for the future London, 20 October 2018 Credit: Angela Christofilou/The Independent Angela Christofilou/The Independent Angela Christofilou/The Independent A historic moment: thousands march to demand Final Say on Brexit Final Say campaigners take part in the peoples vote march for the future in London 20/10/2018 Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Demonstrators pass Trafalgar Square as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Demonstrators wave Union and European flags and hold up placards as they pass Trafalgar Square, taking part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Demonstrators hold placards as they take part in a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit A demonstrator holds a message during a march calling for a People's Vote on the final Brexit deal, in central London on October 20, 2018. - Britons dreading life outside Europe gathered from all corners of the UK to London on Saturday to try to stop their country's looming breakup with the EU. AFP/Getty A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum. PA A historic moment: thousands march to demand Final Say on Brexit Demonstrators take part in the 'People's Vote March for the Future,' in central London, Britain, 20 October 2018. Reports state that the 'March for the Future' is to be led by a column of young people and call for a Peopleâ€™s Vote on the Brexit deal. After marching through central London, there will be a rally on stage in Parliament Square, including speeches from Mayor of London Sadiq Khan EPA A historic moment: thousands march to demand Final Say on Brexit A protester brandishes an Independent t-shirt during the Brexit March Angela Christofilou A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum PA A historic moment: thousands march to demand Final Say on Brexit Tens of thousands of people take part in People's Vote March for the Future in central London. The march organised by the People's Vote campaign is led by young people calling for a People's Vote on the Brexit deal Rex A historic moment: thousands march to demand Final Say on Brexit Anti-Brexit campaigners take part in the People's Vote March for the Future in London, a march and rally in support of a second EU referendum PA

However, Ms Rudd, denied the deal was doomed when it reaches the Commons, arguing MPs would “take a careful look over the abyss” and back it.

“I think likelihood is that, despite what people say, the withdrawal agreement will get through,” the May loyalist told BBC Radio 4’s Today programme.

Ms Rudd has previously argued a ‘Norway-style EEA deal’ – effectively keeping the UK in the EU single market – is an option, if parliament rejects Ms May’s strategy.

She hinted at that approach in the interview, saying: “There will be different amendments that will be followed up on.”

In the summer, Nick Boles, a former Tory minister warned party hardliners that their “dream” of a no-deal Brexit would be blocked by at least 40 fellow Conservatives.

And The Independent revealed in June that they could use a “humble address” – the tactic Labour used to force the government to release Brexit economic assessments – to prevent it.

Earlier, another senior Tory, Damian Collins – who opposes Ms May’s deal – said the public should be given the final say if it is rejected, in either a referendum or a general election.

“I don't think, as parliament, we could just stand back and watch the country fall off the edge of a cliff without asking the people whether that was the step they wanted to take,” he said.

Confirming he will vote against the agreement, Mr Collins said: “I don't accept that this is a deal we have to accept or face the cliff-edge.”

Labour, which has vowed to stop the UK crashing out of the EU without a deal, welcomed Ms Rudd’s acknowledgement that parliament would hold the whip hand.

“Amber Rudd seems to have ignored Number 10’s spin by admitting that Parliament would stop a no deal Brexit,” said Keir Starmer, the party’s Brexit spokesman.