Video report by ITV News Political Correspondent Paul Brand
Theresa May says she is "saddened by the decision," made by the MPs to leave the Conservative party and join former Labour members in a new movement.
Speaking from Brussels after an evening of Brexit talks, the PM thanked the Heidi Allen, Anna Soubry and Sarah Wollaston for the "dedicated service" they gave as members of the Conservative Party.
In the defence of her Brexit negotiations, she said leaving the EU "was never going to be easy," pledging the Conservatives will do "the right thing for the country," by moving forwards with Brexit.
On Wednesday, the self-titled "three amigos" urged other politicians from all sides to join them and eight former Labour MPs who defected to form the Independent Group.
In a joint statement, released via The Independent Group, they said: "The final straw for us has been this Government’s disastrous handling of Brexit".
At a Westminster press conference, they made clear that their concerns about Theresa May's performance went far wider, accusing her of throwing away the modernisation agenda begun by David Cameron and allowing the party to be taken over by right-wing Brexit hardliners.
They added they had left the Conservative Party because "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."
Former prime minister Cameron was among the voices speaking out on the resignations. In a tweet he said he respects "their decision, but disagree with them," adding the Conservatives "need strong voices at every level of the party".
Ms Allen said Theresa May had been "bullied into submission" by the European Research Group of Conservatives and was "dragging the country and Parliament kicking and screaming to the edge of a no deal abyss."
She added: "I can no longer represent a government and a party who can't open their eyes to the suffering endured by the most vulnerable in society, suffering which we have deepened whilst having the power to fix."
In her speech she described Labour defectors as "the magnificent seven", Joan Ryan - another Labour MP who later quit - as "the lone ranger" and called herself, Ms Soubry and Ms Wollaston as "the three amigos".
Following on from Ms Allen, Anna Soubry urged "fellow one nation Conservatives" and "like-minded Lib Dems" to "please, come and join us" in breaking away from their parties.
Also speaking at the press conference was Ms Wollaston, who said the PM had failed to tackle the "burning injustices" in society as promised, adding how the Tories now marching towards the cliff edge of a hard Brexit.
ITV News Political Editor Robert Peston believes the Tory departures means a "general election moves significantly nearer," as the resignations weaken Theresa May's already fragile minority government.
Reaction to resignations:
Responding to the resignations the PM said she was "saddened" but insisted "we are doing the right thing for our country" by delivering Brexit.
She added: "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. Ending that membership after four decades was never going to be easy."
Liberal Democrat leader Sir Vince Cable said his party would "hold out the hand of friendship" to the independents.
He added: "In the short term we will be concentrating on securing a People's Vote, with an option to stay in the EU."
The Independent Group, which with 11 representatives now has as many MPs as the Liberal Democrats, has been described as an 'anti-Brexit party' and its recent statement backs that up.
"Instead of seeking to heal the divisions or to tackle the underlying causes of Brexit, the priority was to draw up 'red lines'. The 48% were not only sidelined, they were alienated," the statement said.
Responding to the exits, pro-Brexit Tory MP Michael Fabricant called on the Government to "deliver the result of the EU Referendum".
He tweeted: "TIG are an anti-Brexit Party. #Labour MPs have joined citing #antisemitism and #Corbyn as the reason. The 3 #Conservative MPs are citing #Brexit.
"Sad to see them go but the Government must deliver the result of #EU #Referendum."
In contrast, former education secretary and Conservative MP Nicky Morgan said she was "very sorry" to see her "principled and fearless friend" Ms Soubry resign.
She tweeted: "Very sorry to read this from my principled and fearless friend @Anna--Soubry - any political party should be a broad church and we should regret losing three such talented women from the Conservative Party."
What happened at Prime Minister's Questions?
During PMQs Theresa May attempted to deflect criticism of the shortcomings in her party by reciting the reasons MPs left Labour.
She said: "I never thought I'd see the day when a once proud Labour Party is accused of institutional antisemitism"
Jeremy Corbyn responded: "There is no place whatsoever in our society or our political parties for antisemitism and my own party takes the strongest action to deal with antisemitism wherever it rears its ugly head".
ITV News Political Correspondent Paul Brand described their exchange as a "pillow fight" and Peston noted the two leaders later opted to talk Brexit in an aim to avoid talking about "the fracturing of their parties".
A split in the Labour Party:
The Tory breakaway comes following a split in Labour which saw eight MPs, led by Luciana Berger and Chuka Umunna, leave their party, citing antisemitism and leadership issues as their reasons.
They were joined on Monday by Chris Leslie, Angela Smith, Mike Grapes, Gavin Shuker and Ann Coffrey before Joan Ryan resigned on Tuesday evening.
Unable to form an official party due to rules and time constraints, the Labour leavers formed what they call The Independent Group and urged MPs from all parties to "leave the old tribal politics behind" and join their new grouping.
Responding to the breakaway, Jess Phillips, the Labour MP for Birmingham Yardley, tried to advise Jeremy Corbyn, saying: "If he doesn't want this crack to become a split, we have to see real determined action on antisemitism as well as other hostilities that exist within the Labour party."
"I'd be lying if I said it doesn't make me feel queasy the thought of staying in a political party where a Jewish woman doesn't feel safe."
She added: "It is not in the gift of people like me, lonely backbenchers like me or Luciana, to shift these things, it is in Jeremy Corbyn's gift and so the baton passes to him now".
Paul Brand understands another Labour MP is reconsidering her future in the party following its reaction to the split.
He tweeted: "Siobhain McDonagh tells me the Labour leadership’s reaction to MPs quitting has been ‘stalinist’ and she’s still considering her future in the party. Sounds very much that unless something changes, she’ll be going too."
If she leaves she will join Joan Ryan as a new Labour Party defector.
Ms Ryan fired a furious broadside at Jeremy Corbyn, accusing him of repeatedly failing to deal with anti-Semitism in the Labour Party.
"We never had this problem in the party before he was the leader. It comes with him, it is part of his politics, I am afraid," she told BBC Radio 4's Today.
"He has introduced or allowed to happen in our party this scourge of anti-Semitism. It has completely infected the party and at every opportunity to deal with it he has not done so."
Ms Ryan, who has represented Enfield North since 1997, with a break from 2010-15, and served as a minister in Tony Blair's government, also attacked Mr Corbyn's position on the EU, claiming he was "aiding and abetting a hard Brexit".
In an apparent response to the defections, Labour launched a consultation on changes to allow voters to force MPs to seek re-election if they swap parties.
An early general election?
While these resignations caused shockwaves within Labour, the Conservative quitters threaten to shake up the current political landscape by diminishing the governments already very weak majority.
The Conservatives are propped up in a confidence and supply agreement with the 10 Democratic Unionist Party MPs, meaning they're bound to vote with the government on issues.
The government's majority has now been reduced by three MPs, meaning the outcome of votes will now be much less certain.
If there is another motion of no confidence in the government, the last of which was narrowly defeated by 325 votes to 306, it may have a different result because three Tory MPs won't have to vote with their party.
The Tory defectors said "there will be times" when they would support the Government at Westminster "on measures to strengthen our economy, security and improve our public services".
"But we now feel honour bound to put our constituents' and country's interests first."
So where do the parties stand now?
Although not a party, the Independent Group now has 11 MPs in the House of Commons - the same number as the Liberal Democrats, and one more than the DUP.
The Conservatives now have 314 MPs, three down on the total won at the 2017 general election.
Labour is down 14 on the general election - the eight MPs who have joined the Independent Group, plus six other MPs who were elected as Labour in 2017 but who now sit as independents.
The combined total for the Conservatives and the DUP is 324, while the combined total for all other MPs is 318.
These figures do not include the seven Sinn Fein MPs who were elected at the 2017 general election, but who do not take their seats in the House of Commons.
The Speaker of the House of Commons, John Bercow, is also not included.
The state of the parties in the House of Commons is now:
Lib Dems 11
The Independent Group 11
Plaid Cymru 4