But the resignations put Mrs May in an even weaker position in Parliament, where her Brexit deal was crushed last month when Eurosceptics and European Union supporters voted against an agreement that both sides say offers the worst of all worlds.
Three Conservative Party MPs, Anna Soubry, Heidi Allen and Sarah Wollaston, on Wednesday joined eight centrist MPs from the left-wing Labour Party, who announced the formation of the Independent Group earlier this week.
Now two more Tory europhiles are threatening to defect: former Attorney-General Dominic Grieve, widely regarded as the ad hoc leader of the "Remain Rebels" in the Tory parliamentary party, and former former education secretary Justine Greening.
A longtime supporter of Palestinian rights and a critic of the Israeli government, Corbyn denies the allegations, saying he is stamping out anti-Semitism in the party. I would not be able to maintain my support of the Government.
Mr Watson said that the eight MPs who resigned from Labour were "valued colleagues" and that it was "a time for reflection and sadness in the Labour Party".
"I want to see a Labour party that's a broad church".
The Tory MPs meanwhile said they were leaving because of a shift to the right by the party, that they blamed in part because of the influence of the European Research Group - a group of pro-Brexit Tory MPs.
"I think that Brexit has absolutely fractured British politics and that includes the Conservative Party".
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It's not unthinkable that a copy of Super Mario Bros . like this one could eventually be worth that much. One of the game's buyers, Jim Halperin , didn't rule out selling the copy of Super Mario Bros . on.
The Independent Group was formed by seven ex-Labour MPs, including Chuka Umunna and Luciana Berger, and was joined by and eighth MP on Tuesday.
Scottish Labour leader Richard Leonard has issued a call for unity and insisted Jeremy Corbyn's "unifying vision" was the reason behind the party's fightback north of the border.
Mrs May said she was "saddened", but her party would "always offer. decent, moderate and patriotic politics". In the meantime, South Cambridgeshire Conservatives need to unite and focus on ensuring that the next MP for South Cambridgeshire is a Conservative MP.
"I believe this to have been a foolish decision".
Mr Woolfe said: "I think a whole lot of things, let's start with Tony Blair, I was on the march with those who said we shouldn't go to the war in Iraq".
It is with regret that we are writing to resign the Conservative whip and our membership of the Party. "At a time when the country is suffering from a hopeless and aimless Conservative government, I am confident that the overwhelming majority of Labour representatives and members will continue to concentrate on building the alternative the country desperately needs". We had to put our values and principles ahead of our positions'.
Members of the new group have indicated they will resist demands from the leadership, including shadow chancellor John McDonnell, to step down and seek a fresh mandate from voters in a by-election. Douglas Carswell, who resigned from the Conservatives to join UKIP in 2014, tweeted: "When I changed parties it didn't occur to me to not hold a by election". But we now feel honour bound to put our constituents' and country's interests first.