Downing Street has said it is “extremely concerning” that MPs could attempt to override the government to suspend or delay the article 50 process to leave the EU in their effort to prevent a no-deal Brexit.

A slew of backbench amendments are expected to be attached to the prime minister’s statement on Monday on the way forward for the Brexit withdrawal agreement.

The Conservative MP Nick Boles and Labour’s Yvette Cooper will also put forward an amendment to attempt to change House of Commons timetabling rules. The change would pave the way for their proposed bill to extend article 50 in the absence of a deal to take precedence over other Commons business.

Quick guide Brexit and backstops: an explainer Show Hide A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

The former attorney general Dominic Grieve is also reported to have sought advice from a senior Commons clerk about how MPs might stop or suspend the two-year process.

One of his proposals, which would go further than Cooper and Boles’ plan, is that changing the timetable of the Commons should need the support of only 300 MPs – far from a parliamentary majority – as long as they come from five different parties, including at least 10 Tories.

A No 10 spokesman said there was deep unease at the wider implications of such amendments. “Any attempt to remove the government’s power to meet the legal conditions of an orderly exit at this moment of historic significance is extremely concerning,” he said.

“This news should serve as a reminder to those MPs who want to deliver Brexit that they need to vote for it, otherwise there is a danger that parliament could stop Brexit.”

Labour’s Hilary Benn and the Conservative MP Nicky Morgan, who are backing efforts for parliament to block a no-deal Brexit, both defended the action on Sunday.

“MPs doing their job are not plotters, they are trying to sort out the mess the prime minister has created,” Benn told BBC One’s The Andrew Marr Show.

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“We are facing a national crisis, and there are many MPs in the House of Commons whose first priority is to ensure that we do not leave without a deal and therefore finding ways when we come to table amendments this week and debate on 29 January how we stop that.”

Benn said it was “a disgrace” to criticise Commons clerks who had advised MPs, saying they were “resolutely impartial”.

Morgan, who has signed the bill put forward by Cooper to delay article 50 in the absence of an agreement, said it was not a secret plot by MPs but an attempt to act in the national interest.

“The bill I’ve put my name to does say that if the government can’t get an agreement in place then the minister would have to apply to say to Brussels, right, we need to suspend article 50 for a period of time so that we can build a consensus and get ourselves more prepared for exit,” she told Sky’s Sophy Ridge on Sunday.

“As other MPs have said, it’s a strange coup that starts with a whole bunch of democratically elected members of parliament. I think the prime minister is in, I think the government is in, an incredibly difficult position.

“We’re going to find out more I think this week, certainly next week, about the prime minister’s plan B, and then I think we’ll all have to make decisions as MPs about what’s in the national interest.”

MPs hoping to prevent a no-deal Brexit were due to meet on Monday afternoon in Benn’s office to discuss the best route forward. May is to update her cabinet ministers in a 5pm conference call on the substance of her discussions since losing the Commons vote on Tuesday.

The international trade secretary, Liam Fox, said such moves would put MPs at odds with the public.

“You’ve got a leave population and a remain parliament. Parliament has not got the right to hijack the Brexit process, because parliament said to the people of this country, we make a contract with you, you will make the decision and we will honour it,” he said.

“What we are now getting is some of those who always absolutely opposed the result of the referendum trying to hijack Brexit and in fact steal the result from the people.”

Fox said the route to a compromise on the Brexit deal lay with Tory backbenchers, hinting the government was exploring the possibility of a joint UK-Irish treaty that would replace the backstop, as reported in the Sunday Times. The plan is favoured by some hard Brexiters including the former cabinet minister Owen Paterson.

“We have to compromise on the backstop, if we’re to get the agreement through we absolutely have to do that; the question is how we find a way to do that,” Fox said, adding that he favoured a different mechanism to prevent a hard border.

But Irish sources said the government would reject any approach from May for a bilateral side deal, calling the idea a “non-starter”.

Sources in Dublin said the EU was “very clear” the withdrawal agreement could not be reopened unless May changed her red lines.

Simon Coveney (@simoncoveney) As #Brexit dominates news coverage, no surprise that some analysis today gets it wrong. I can reassure you the Irish Govt’s commitment to the entire WA is absolute - including the backstop to ensure, no matter what, an open border between Ire + NI and the #GFA are protected. pic.twitter.com/ToAt6o0B6P

The Irish foreign minister, Simon Coveney, said: “I can assure you that the Irish government’s commitment to the entire withdrawal agreement is absolute, including the backstop to ensure, no matter what, an open border between Ireland and Northern Ireland, and the Good Friday Agreement, are protected.”

A source said: “The solidarity in the EU is complete there, as Donald Tusk and Jean-Claude Juncker made clear; they are waiting to see what Theresa May’s plan B is. From our perspective, a bilateral deal is just not a credible proposal.”