Three British MPs quit the governing Conservative Party over Brexit on Wednesday, joining a mounting rebellion in parliament this week against the two major parties that is shaking the system in British politics.

Anna Soubry, Heidi Allen and Sarah Wollaston said they planned to sit in parliament alongside eight former Labour MPs who, also citing their opposition to Brexit, have resigned from the main opposition party since Monday to form the new Independent Group.

The trio of Conservatives, who support Britain remaining in the European Union, said in a joint resignation letter to Prime Minister Theresa May that Brexit had "re-defined" their party and was "undoing all the efforts to modernise it".

"The final straw for us has been this government's disastrous handling of Brexit," they added, in stinging criticism of May's leadership, noting they could "no longer act as bystanders" to her EU exit strategy.

"Following the EU referendum of 2016, no genuine effort was made to build a cross-party, let alone a national consensus to deliver Brexit."

The resignations posed a fresh and embarrassing headache for the prime minister as she prepared to travel to Brussels later Wednesday for crucial talks with European Commission President Jean-Claude Juncker.

It also reinforced the view that Britain was plunging further into political turmoil as its MPs struggle to agree a divorce deal just five weeks before it is due to leave the bloc on March 29.

The political impasse risks the country crashing out without an agreement, with the rising uncertainty blamed for a string of car-makers and other businesses recently announcing job cuts and reduced investment in Britain.

May said she was "saddened" by the resignations and thanked the MPs for their "dedicated service to our party over many years".

She noted Britain's membership of the EU has been "a source of disagreement both in our party and our country for a long time" but the MPs' move would not stop her delivering on the referendum result. 

"Under my leadership, the Conservative Party will always offer the decent, moderate and patriotic politics that the people of this country deserve," she added.

- 'Radical changes now afoot' -
Earlier Wednesday, an eighth MP quit the Labour Party in protest against its veteran socialist leader Jeremy Corbyn, joining its own growing internal rebellion sparked by rows over Brexit and anti-Semitism.

Joan Ryan told BBC radio that Corbyn had "introduced or allowed to happen in our party this scourge of anti-Semitism. It has completely infected the party".

The shake-up of seats mean May's centre-right Conservatives alone are now six votes short of a majority in parliament's lower House of Commons.

They can command a working majority of eight thanks to their confidence and supply arrangement for support from Northern Ireland's 10 Democratic Unionist (DUP) lawmakers.

Meanwhile The Independent Group now form the joint fourth-biggest bloc in the Commons with 11 MPs -- the same as the centrist Liberal Democrats, with predictions of further defections to come.

The new group sat squashed together on the opposition backbenches in the Commons during the prime minister's weekly grilling, but did not ask May a question.

Liberal Democrat leader Vince Cable said: "There is clearly some very radical changes now afoot as both the Conservatives and Labour have been taken over by militant groups, driving out more moderate MPs."

- 'Country's interests first' -
In their resignation statement, the three former Conservative MPs, who have voted against multiple elements of the government's Brexit legislation, blamed their decision on May's "dismal failure" to stand up to the "hard line" European Research Group (ERG) of Brexiteers in her own party.

The group "operates openly as a party within a party, with its own leader, whip and policy" they said.

"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 lawmakers added.

They noted that there was a wider dissatisfaction with the state of British politics, with both the Conservatives and Labour moving "to the fringes, leaving millions of people with no representation".

"We now feel honour bound to put our constituents' and country's interests first," they added. 

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