- Business minister Richard Harrington announced his decision to leave government on Twitter.
- MPs will now have the chance to vote on various options, such as revoking Article 50 and cancelling Brexit.
- May admitted Monday she had still not secured the votes needed to get her own, twice-rejected Brexit deal through parliament.
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.