LONDON — Under normal circumstances, the British lawmakers Nick Boles and Yvette Cooper would hardly be called rebels.
Mr. Boles, an Oxford-educated Tory, comes from a long line of colonial officers and Conservative Party stalwarts. Ms. Cooper, an Oxford-educated Labour lawmaker, became a government minister at the age of 30, and was the first woman to serve as chief secretary to the Treasury.
But on Tuesday, these two moderate, establishment lawmakers, both representing districts that strongly backed Britain’s exit from the European Union, hope to present the British government with a historic challenge.
They plan to propose an amendment in Parliament that could delay Britain’s departure from the bloc for a few months or even until the end of the year rather than leave without a deal.
It will be a day of muscle-flexing on Tuesday in Parliament, in which opposition and backbench lawmakers — traditionally the system’s weaker players — will try to take a greater degree of control over Brexit, as the process of leaving the European Union is known.
[Read more about how the amendment process works.]
The Cooper-Boles amendment, if it is passed, would be a game-changer, insulating Britain from the economic shock of a uncontrolled departure, a so-called no-deal Brexit.
It would also undermine Prime Minister Theresa May, who hopes to use the threat of a no-deal exit to extract 11th-hour concessions from Irish and European negotiators.
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As Tuesday approached, both Ms. Cooper and Mr. Boles had received threats from constituents who saw them as endangering Brexit.
“I think they are taking a very big risk,” said Ayesha Hazarika, a political commentator and former adviser to Labour Party politicians.
“The grass roots, both Labour and Conservative supporters, will look at the two of them, and the words ‘traitor’ and ‘betrayal’ will come from their mouths,” she said. “This amendment will come at a high personal cost to both of them.”
Tuesday’s likely votes on this and other amendments will be a test of Parliament’s ability to shape policy, for many decades the exclusive domain of the executive branch.
Mr. Boles on Monday invoked the 19th-century political scientist Walter Bagehot, who wrote that the House of Commons has control over its procedures, and can change them by majority vote.
But Mrs. May’s team spent much of Monday pleading with centrist Conservative lawmakers not to support the Cooper-Boles amendment, assuring them that they will have an opportunity to prevent a no-deal Brexit in February, when the prime minister brings a revised version of the deal back to Parliament.
Instead, Mrs. May is encouraging Tories to support an amendment proposed by Graham Brady, a senior Conservative lawmaker, who has called for changes to the backstop, a plan to keep goods flowing across the Irish border without customs checks — in effect, tying Britain to European Union trading rules for a limited amount of time.
While his proposed amendment is vague, pro-Brexit Conservatives favor a time limit to the backstop plan or a unilateral right to leave it.
That solution presumes concessions from the European Union, whose officials have ruled out significant moves. Sabine Weyand, the European Union’s deputy chief negotiator, on Monday said a time limit on the backstop “defeats the purpose.”
“Once the backstop expires, you stand there with no solution for this border,” she said, speaking in Brussels, Reuters reported.
On Friday, Mr. Boles spent two hours addressing a largely critical crowd of Conservative activists in his home constituency of Grantham and Stamford in Lincolnshire, which voted 61 percent to leave the European Union.
Philip Sagar, the constituency party chairman, said Mr. Boles would “probably not get reselected” if his candidacy came up for a vote now, because he was seen as diverging from the majority.
“When we elect an M.P., they have to represent the whole of his or her constituency,” Mr. Sagar said. “Parliament overwhelmingly abrogated their authority on the future of Europe to the people, and the people voted to leave.”
Mr. Boles told the BBC he had received a string of threats from unhappy Brexiteers.
“A couple of days ago somebody called my office and said they were going to burn my house down,” he said. “I feel like I’m bound to get one of those vile treatments from one of the particularly unpleasant characters in ‘Game of Thrones.’”
The proposed amendment, though, picked up support from Eliza Manningham-Buller, the former head of one of Britain’s security agencies, MI5, who told the BBC that a no-deal exit would compromise Britain’s security by cutting off access to European databases and joint mechanisms.
She rejected the notion that Parliament was overstepping its bounds.
“It seems to me that there’s an irony here,” she said. “The Brexiters — and I’m not one of them — argue that it’s about taking back parliamentary sovereignty. If it’s about parliamentary sovereignty, Parliament is sovereign.”
A number of leading supermarket and restaurant chains on Monday released a letter warning that consumers could experience shortages and face higher prices in the event of a no-deal exit.
The letter to lawmakers, signed by Marks & Spencer, McDonald’s, Sainsbury’s and others, said that stores were stockpiling where possible but that all frozen and chilled storage was already being used, and that “even if there were more space it is impossible to stockpile fresh produce, such as salad leaves and fresh fruit.”
Among the complications for lawmakers is that Parliament views a no-deal Brexit with far more apprehension than the general public, said Tony Travers, a professor of government at the London School of Economics.
In a poll taken this month by YouGov/Best for Britain, 31 percent of respondents said they would prefer to leave the European Union without a deal, compared with 36 percent who would choose a second referendum and 16 percent who did not know what to do.
Among members of the Conservative party, the proportion preferring a no-deal exit rises to more than half, according to a December poll.
“This is a culture war issue,” Mr. Travers said. “It’s a very, very awkward position to be in, because you have to go against your constituents in order to protect them — even though they say they want no deal.”