A group of anti-Brexit MPs split off from their respective parties this week, shaking up British politics just as the country seeks to secure its departure from the European Union next month.

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. The group of Labour MPs are more traditionally aligned with former Prime Minister Tony Blair's centrist version of the Labour Party that swept to power in 1997.

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The Labour MPs had cited left-wing leader Jeremy Corbyn’s handling of both Brexit and rising anti-semitism within the party since he came to power in 2015.

“Over the past three years...the Labour Party under Jeremy Corbyn has become infected with the scourge of anti-Jewish racism,” a statement by MP Joan Ryan said. “This problem simply did not exist in the party before his election as leader. No previous Labour leader would have allowed this huge shame to befall the party.”

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.

“Brexit has re-defined the Conservative Party – undoing all the efforts to modernize it,” a letter to Theresa May said. “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.”

The new group is not yet a party, but the group of rebels sat on the independent benches of the House of Commons on Wednesday. They are likely to face calls from angry Labour and Tory members to put their seats up to a challenge in by-elections.

It is unclear what effect the new group will have on any upcoming general elections, which could come as early as this year. Initial polls have shown that the Independent Group could command up to 14 percent of votes from the electorate, eclipsing the Liberal Democrats, the traditional third party of British politics.

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How that would translate into seats would depend on where the votes were cast and how many Independent Group MPs were running. It could potentially lead to either a group of Independent MPs winning office, or it splitting the anti-Brexit vote and handing a lead to the broadly pro-Brexit Tories.

The Tory rebels announced their split just as Prime Minister Theresa May is in Europe attempting to renegotiate her withdrawal agreement with E.U. leaders. E.U. leaders have expressed skepticism about the potential for a re-negotiation, but in a joint statement on Wednesday, May and E.U. Commission President Jean-Claude Juncker said that talks had been "constructive."

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The deal was shot down by Parliament last month, leading to a scramble to re-negotiate the deal, or possibly extend Britain’s date for departure before Britain is set to leave the bloc without a deal at the end of March.

Brexit hardliners have said that no such deal is needed, noting that Britain would revert to World Trade Organization trading terms with the E.U. However, pro-Remain MPs -- including those in the new bloc -- have called for a delay or even a second Brexit referendum to re-do the 2016 Brexit vote.