The trio of Tory defectors - Anna Soubry, Heidi Allen and Sarah Wollaston - are among the Conservatives" most well-known and outspoken "Remain' voices, and like their new ex-Labour crossbench colleagues they want a second referendum that they hope might overturn the outcome of the first.
They could also undermine Mrs May's negotiating position in Brussels, where she is going later on Wednesday (local time) for talks with European Commission President Jean-Claude Juncker to try to secure an opening for further technical work on revising the agreement.
"This problem simply did not exist in the party before his election as leader".
Soubry centred many of her remarks on the Brexit negotiations, and appealed directly to those in the Conservative government opposed to "no deal" to take drastic action.
Their letter to the Prime Minister says: "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".
The seven Labour PMs are not launching a new political party but have urged other Labour MPs - and members of other parties - to join them in "building a new politics".
During the Q&A the MPs also said there may be other resignations from both the Conservative and Labour parties.
He said: "I'm sticking with him because as a Labour Party member for over 35 years, we are a broad movement with over half a million members who democratically elected him twice".
Luciana Berger, one of the founders of the Independent Group, exited Labour after speaking out about anti-Semitism in the party.
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Foreign Secretary Jeremy Hunt said he hoped they would be "welcomed back" if the government could demonstrate Britain remained an open and outward looking country after Brexit.
The resignantions began on Monday when seven Labour MPs quit.
The compromise, named after Tory MP Kit Malthouse, and championed by cross-factional MPs including Eurosceptic Steve Baker and soft Brexiter Nicky Morgan, may have seen the prime minister win the support of the European Research Group, led by Jacob Rees-Mogg - Rees-Mogg has previously given his full support to Malthouse.
Rebel MPs from the Independent Group will formally meet the Liberal Democrats to discuss Brexit.
"People holding those views have no place in the Labour Party", he wrote. We've seen this exchange before, more than once, but now 29th March is just over a month away. A party of economic competence, representing the best of British business, delivering good jobs, opportunity and prosperity for all, funding world class public services and tackling inequalities.
Following Wednesday's announcement that the three Tory MPs were joining them, along with another former Labour MP, Joan Ryan, a survey by YouGov had the group on 14 per cent.
Although the Independent MPs may benefit from some personal support, all of their constituencies - with the exception of Angela Smith's Penistone and Stocksbridge and Ms Ryan's Enfield North - are rock-solid Labour seats which would need a substantial swing to change hands.
"That's why I am so disappointed they have gone and that's why I really want people to stay and fight their corner".
"I am determined that under my leadership the Conservative Party will always offer the decent, moderate and patriotic politics that the people of this country deserve".