The Brexit process has grown increasingly surreal since Parliament rejected Mrs May's divorce deal two weeks ago, leaving Britain lurching towards a cliff-edge "no-deal" departure from the bloc on March 29.
A spokesperson for the British Retail Consortium (BRC) declined to comment on the BBC report but said the group had previously warned of the risks of a no-deal Brexit, including the possibility of higher food prices.
Another danger for the prime minister is that pro-Remain Conservative MPs may back an amendment by Labour's Yvette Cooper which would potentially delay Brexit.
The government said that this second "meaningful vote" would also be amendable, possibly convincing some MPs not to take any drastic action on Tuesday, knowing they will have another chance.
Any act of parliament, excluding the Human Rights Act, can also be suspended for up to 21 days.
"And Graham has said he could live with a protocol rather than changes to the text, whereas from our point of view there needs to be changes to the text".
Amid the bitter wrangling Queen Elizabeth II appeared to make a rare foray into politics last week, emphasising in a speech the need for Britons to come together to "seek out the common ground".
Sinn Féin has said there is no room to change any aspect of the backstop in the Brexit Withdrawal Agreement and that Irish politicians would not be to blame in the event of a hard border in Ireland resulting from a "no deal" Brexit.
May insists her agreement can still win Parliament's backing, if it is tweaked to alleviate concerns about the border measure, known as the backstop.
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It was far from certain the amendment would win support from a majority in the House of Commons. There is now no clear agreement for how the United Kingdom will leave the bloc that has the support of both Parliament and other European states.
Today's votes will not mark the end of Britain's turmoil over Brexit. It was the biggest government defeat in the House of Commons for more than a century and prompted two weeks of soul-searching and debate over how to resolve the impasse inside the government.
The prime minister told her Cabinet today she was ready to reopen negotiations with the European Union on the Brexit Withdrawal Agreement to secure changes to the controversial backstop plan to avoid a hard border in Ireland.
In one exchange, confirmed to Sky News by a close ally, Mr Johnson shouted at the PM: "What do YOU want to do, Prime Minister".
Mrs May had urged MPs to back a different amendment that would propose "alternative arrangements" to the controversial Irish backstop plan, saying it would give her a "mandate" to secure a "legally binding change" in the EU.
Ms Weyand said the ratification of the EU-UK deal would build the trust necessary to build a new relationship, but ruled out bowing to British calls to set a time limit to the backstop beyond which the insurance policy would lapse.
The backstop is meant to avoid a hard border between Ireland and Northern Ireland, but so-called "Brexiteers" have pointed to the lack of a unilateral exit mechanism as evidence that the backstop could lead to Britain never leaving the bloc.
In a joint letter, leading retailers including Sainsbury's, Asda and Waitrose warned that quitting the European Union without a Withdrawal Agreement on March 29 would risk driving up food prices and cutting the range and quality of products on supermarket shelves.
"It allows the PM to give a very clear message about what the parliament wants and where the party is", Lewis said.
"Labour's amendment. starts by calling for sufficient time for Parliament to vote on options that prevent leaving with no deal", he said.