Many Labour politicians are unhappy with the party's direction under leader Jeremy Corbyn, a veteran socialist who took charge in 2015 with strong grass-roots backing.
Member of Parliament Luciana Berger announced the resignations, saying that she had become ashamed of what the party had become after it was, in her words, "hijacked by the extreme left".
Luciana Berger, Chris Leslie, Angela Smith, Gavin Shuker, Mike Gapes, Ann Coffey and Chuka Umunna will now sit in an "Independent Group" they want to become a new force in United Kingdom politics.
They billed themselves "the Independent Group" at the Monday press conference.
Commenting on suggestions MPs could again quit Labour to join a breakaway party, Mr McDonnell told the BBC's Andrew Marr Show: "It would be like the 1980s because my constituency in Hayes and Harlington - we had a Labour MP join the SDP and we lost the seat to the Conservatives".
Eurosceptics in Prime Minister Theresa May's Conservative Party flexed their muscle by voting against her government in a symbolic Brexit ballot last week but have so far given little sign of formally breaking away.
London Mayor Sadiq Khan called it a "desperately sad day", despite agreeing that the public should be allowed to re-litigate Brexit and that anti-Semitism needed to be addressed within the party.
"Now more than ever is the time to bring people together to build a better future for us all", he added.
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Iranian Foreign Minister Mohammad Javad Zarif has called the two-day meeting a "desperate anti-Iran circus" and has kept up a steady stream of tweets mocking it in English.
In photos taken a year before Corbyn was elected as the leader of the Labour Party, he is seen holding a wreath over the grave of Atef Bseiso, the head of intelligence for the Palestine Liberation Organization (PLO), who helped plan the attack at the Munich Olympics, which claimed the lives of 11 Israeli athletes. The necessary first step will be for Mr Corbyn to apologise for his past comments and affiliations with Jew-haters and to expedite urgently the disciplinary process against all Labour Party members accused of antisemitism.
In her email, Formby offered details on the extent of anti-Semitism complaints between April 2018 and January 2019, saying 673 complaints were received by party institutions about Labour members.
It follows disquiet over how the Labour leadership has handled the party's position on Brexit and concerns over anti-Semitism.
Labour's deputy leader Tom Watson urged those thinking of quitting to "stay and fight their corner".
"The values we hold mean that, in all conscience, we can have no confidence in the party's collective leadership, competence or culture", the group's statement said. He said that there was "no need to split".
"The Labour party we joined and campaigned for and believed in is no longer today's Labour Party", Leslie told reporters.
The president of the Board of Deputies of British Jews, Marie van der Zyl, said: 'This is a moment of great shame for the Labour Party and a tragedy for the thousands of Jews who have supported the party for generations'.
She added: "I can not remain part of party that I have come to the sickening conclusion is anti-semitic".