The warning came as Theresa May addressed senior ministers at a special meeting of Cabinet ahead of a historic week of crunch votes in the House of Commons which could shape the outcome of Brexit.
Mrs May is facing a battle to hold on to power as MPs seek to seize control of parliamentary business in a bid to secure a softer Brexit, while some of her own backbenchers openly discuss her removal as Prime Minister.
In its statement, the European Commission said it had completed its preparations for a possible no-deal Brexit, but warned it would nonetheless cause “significant disruption for citizens and businesses”.
If it crashes out without a deal on April 12, the UK will not benefit from a transition period to new arrangements, but will immediately be subject to checks and tariffs on its exports to the EU, while “significant delays” can be expected at the borders, said officials.
Following an oral statement from the PM updating them on the decision reached at last week’s EU summit to extend the Brexit negotiation period beyond March 29, MPs are due to vote on a proposal to force a series of indicative votes on alternatives to her Withdrawal Agreement.
Defeat for the Government on Monday night over the plan - tabled in an amendment by former ministers Sir Oliver Letwin and Dominic Grieve and Labour MP Hilary Benn - would be a further humiliation for Mrs May.
The proposal seeks to pave the way for a series of indicative votes in the Commons on Wednesday, effectively taking control of the Brexit process out of the hands of the Government.
Sir Oliver acknowledged that any votes would be advisory rather than binding on the Government and it may take several rounds of voting before a majority is found for any of the options - if one can be found at all.
He said Mrs May “hasn’t been able to get a majority and we don’t know what she could get a majority for, so once we find that out there is a way forward, in principle, and then the next thing would be for the Prime Minister to take that forward and for the Government to implement it”.
But he told BBC Radio 4’s Today: “None of us know whether it will work.”
Tory backbencher Nigel Evans, a joint executive secretary of the influential Conservative 1922 Committee, said Theresa May should set out her plans to quit in order to get her Brexit deal through.
“Clearly a number of people do not want the Prime Minister anywhere near the next phase of negotiations, which is the future trading relationship between ourselves and the EU,” he told Today.
He said there should be an “orderly” process to replace the Prime Minister, with a full leadership contest rather than an interim successor.
And Mrs May’s former Downing Street director of communications, Katie Perrior, said it was time for the Prime Minister to announce her departure date to get her Brexit deal through.
Writing in The Times Red Box, Ms Perrior said: “Maybe it’s time to stop finding scapegoats and admit that Theresa May and her lack of leadership has made a bad situation worse.
“With great sadness, it’s time for her to swap her departure date in return for the deal. It’s the least she can do.”
But International Trade Secretary Liam Fox insisted that Mrs May was respected by the public, despite calls for her to go from MPs.
“What I was finding from real voters was people spontaneously saying: ‘I don’t understand how Theresa May puts up with the pressure, she is a great public servant, her resilience is amazing’,” Dr Fox told Today.
“There seems to me to be a bigger disconnect now between Westminster and what is happening out in the country than ever before.”
He said Tory Eurosceptics had to accept that MPs would block a no-deal Brexit.
“For a lot of my colleagues, I think they still believe there is a route to no-deal,” said Dr Fox. “I have come to the conclusion some time ago that was unlikely given the House of Commons that we have.
“I think we will see today that there is a mood in the House of Commons to stop us leaving without a deal, even if that means no Brexit. I think that is a constitutionally disastrous position.”
On Sunday, Mrs May held “lengthy” talks with prominent Brexiteer backbenchers including Boris Johnson, Jacob Rees-Mogg and David Davis at her country residence Chequers to discuss whether there is sufficient support among MPs for another vote on her deal.
But Mr Johnson claimed the Government had “chickened out” of delivering Brexit this week.
And he signalled his belief in the need for a change of leadership by asking in an article in the Daily Telegraph: “Can we really go on with a negotiating team that has so resoundingly failed?”
If Mrs May cannot deliver “convincing proofs” of how the next phase of the negotiations will be different from the last, he said she should “drop the deal, and go back to Brussels, and simply set out the terms that so many on both sides - Remainers and Leavers - now believe are sensible,” wrote the former foreign secretary.
“Extend the implementation period to the end of 2021 if necessary; use it to negotiate a free trade deal; pay the fee; but come out of the EU now - without the backstop. It is time for the PM to channel the spirit of Moses in Exodus, and say to Pharaoh in Brussels - let my people go.”
Meanwhile, The Sun newspaper used its front page on Monday to urge Mrs May to promise to resign in order to win support for her deal from Tory Brexiteers and the DUP.
“Unlike so many she has determinedly respected the will of the Leave majority... She must now take the next principled step - and show she is not just another craven politician determined to cling to power,” it said.