At a news conference after their defection, they said others were likely to join them.
While this new Independent Group on its own will not be able to stop Brexit, analysts say, it may play an outsize role in stopping a so-called "no-deal Brexit," under which Britain would crash out of the continental trading bloc without any transition period or trade deal.
The defectors left their parties for different reasons, but opposition to Brexit unites them. The centrist members who abandoned Jeremy Corbyn's Labour Party say their movement has swung too far left.
When they resigned on Tuesday and yesterday, the eight Labour defectors complained about Corbyn's handling of Brexit and his inability to stamp out anti-Semitism in the party.
The three Conservatives, or Tories, who broke away today blamed their party's "failure" to stand up to zealous Brexiteers, specifically the gathering of approximately 60 backbenchers known as the European Research Group, or ERG, who are pushing for a complete break from the European Union.
The leaders of the ERG, who have failed to topple May, say they would rather see a "no-deal Brexit" than preserve the relative compromise and closer ties that May seeks on rules and regulations.
The Tory defectors also complained about the disproportionate power of Northern Ireland's Democratic Unionist Party, or DUP, which is propping up May's minority government after her disastrous showing in the 2017 snap elections. The DUP - dominated by Protestant loyalists - rejects any compromise that would threaten Northern Ireland's position in the United Kingdom.
Announcing their resignations, the three Tories - Sarah Wollaston, Heidi Allen and Anna Soubry - told the Prime Minister in a statement, "We no longer feel we can remain in the Party of a Government whose policies and priorities are so firmly in the grip of the ERG and DUP."
They wrote: "Brexit has redefined the Conservative Party - undoing all the efforts to modernise it. There has been a dismal failure to stand up to the hard line ERG which operates openly as a party within a party, with its own leader, whip and policy."
At a news conference, Allen complained that May and the Conservative Party were being "bullied into submission" by hardline Brexiteers such as former foreign secretary Boris Johnson.
Wollaston said the Conservatives were no longer the "tolerant, moderate, openhearted" party of the past, but have been taken over by the hard right, which she claimed "is marching us toward the cliff edge of a no-deal Brexit."
In announcing her resignation, Soubry said, "The right-wing, hardline, anti-EU squad are now running the Conservative Party, from top to tail."
Soubry said this "purple movement" - blending the colours of "two broken parties," red Labour and blue Conservative - would likely attract more converts and may someday become its own political party rather than a voting bloc.
"Please, come join us," she said, predicting that more ministers in May's Cabinet would soon resign their posts - if not their parties - over the prime minister's handing of Brexit.
The resignations came as May shuttled to Brussels for another round of talks on how Britain could leave the EU but preserve open borders in Ireland.
May said she was "saddened" by her colleagues' decision to leave the party. "These are people who have given dedicated service to our party over many years, and I thank them for it," she said.
The prime minister acknowledged, too, the obvious, that Brexit is painful and hard. "Of course, the UK's membership of the EU has been a source of disagreement both in our party and our country for a long time," May said. "Ending that membership after four decades was never going to be easy."
But May said she and the Government would press on and deliver the Brexit that the country voted for in a June 2016 referendum.
Tony Travers, a politics professor at the London School of Economics, noted that the Independent Group now rivals in size the Democratic Unionist Party and Liberal Democrats party.
The new bloc "slightly reduces the power of both the government and the opposition," Travers said. "It makes an accidental no-deal Brexit fractionally less likely, too."
How this changes the dynamics of upcoming votes on Brexit is unclear.
It remains possible that Britain will crash out with no deal, or that Britain will seek a delay beyond the March 29 deadline, or that more negotiations will be undertaken, or that citizens will be asked to vote again on whether - now knowing all they know - they really, really want to leave the EU.
