Foreign Office minister Alistair Burt and health minister Steve Brine resigned, while business minister Richard Harrington announced his decision to leave government on Twitter
British MPs voted on Monday to play a bigger role in Brexit, giving themselves the power to express their preference for different options in an unprecedented move that the government called "dangerous".
MPs won a vote that will allow them to seize control of parliamentary business on Wednesday by 329 to 302, with three junior ministers quitting after voting against the government.
Foreign Office minister Alistair Burt and health minister Steve Brine resigned, a government source told AFP, while business minister Richard Harrington announced his decision to leave government on Twitter.
In his resignation letter, Harrington said the government's approach was "playing roulette with the lives and livelihoods of the vast majority of people in this country".
But the Brexit ministry said in a statement it was "disappointed" by the vote, adding that it "upends the balance between our democratic institutions and sets a dangerous, unpredictable precedent".
Three years after Britain voted to leave the European Union, Monday's vote sets up a potentially crucial clash between government and parliament on the best way of ending a bitter political crisis.
MPs will now have the chance to vote on various options, such as revoking Article 50 and cancelling Brexit, holding another referendum, a deal including a customs union and single market membership or leaving the EU without a deal.
But even if MPs decide a majority course of action, the government is not legally bound to follow their instructions.
"The government will continue to call for realism -- any options considered must be deliverable in negotiations with the EU," the Brexit ministry said.
The prime minister earlier said she was "sceptical" about the process, saying similar efforts in the past "produced contradictory outcomes or no outcomes at all".
May admitted Monday she had still not secured the votes needed to get her own, twice-rejected Brexit deal through parliament, raising again the prospect that Britain could crash out of the European Union in just over two weeks' time.
Anxious at the deepening crisis in London, EU leaders last week agreed to postpone Brexit to avoid a potentially catastrophic "no deal" divorce on March 29, when 46 years of ties were formally scheduled to end.
But they warned that unless May can persuade MPs this week to support her withdrawal deal, Britain must come up with a new plan by April 12 -- or leave its closest trading partner with no deal at all.
Opposition Labour leader Jeremy Corbyn said the government was a "national embarrassment", adding: "We will still face the prospect of a disastrous no-deal Brexit."
The EU had earlier ramped up the pressure by announcing its full readiness to deal with the "increasingly likely" event of a no-deal Brexit in three weeks' time.
The British parliament remains deeply divided over Brexit, reflecting the sharp divisions in the country.
MPs have already voted against a "no deal" Brexit but this remains the default legal position unless they agree an alternative.
May went over her own Brexit scenarios at an emergency cabinet meeting earlier Monday.
It followed a weekend of media reports that her own ministers were trying to oust her.
Most of the alleged plotters are Brexit backers who fear the terms of Britain's departure will be watered down or even reversed.
"Theresa May is the chicken who bottled Brexit," former foreign minister Boris Johnson wrote in a weekly column for The Telegraph.
"It is time for the PM to channel the spirit of Moses in Exodus, and say to Pharaoh in Brussels – LET MY PEOPLE GO," he wrote, leaving some room however for possibly supporting her deal.
What happens to her premiership if parliament favours a more EU-friendly Brexit alternative that contradicts her policies is unclear.
Parliament is thought most likely to rally around the idea of keeping Britain in a customs union with the European Union or its single market.
Both of those policies contradict May's position.
A customs union would keep Britain from striking its own trade agreements with non-EU countries.
A single market would require the government to go back on May's promise to regain control of Britain's borders and migration policy.