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Momentum was set up to support Jeremy Corbyn's leadership campaign. However, some Labour MPs believe it is being used as a device for a far-left takeover of the party.
Momentum is heavily populated with members of the Trotskyist group the Alliance for Worker's Liberty and is accused of plotting to deselect centrist Labour MPs.
One Labour MP who has been highly critical of Corbyn's leadership, told Business Insider that he would fight any attempt to affiliate Momentum to Labour.
"I will be opposing this with every fibre of my body," the Labour MP, Tom Blenkinsop, said.
Former Labour leadership contender Owen Smith has previously called for all Momentum members to be banned from being Labour members. In comments which compared the group to a parasite, he said: "There is nothing comradely about setting up party within a party." "Still less in trying to use our movement as a host body, seeking to occupy it, hollow it out, until it's outlived its usefulness, when you throw it aside like a dead husk."
The group's founder Jon Lansman emailed members last night to announce that they had decided to move towards affiliating with Labour. In the email seen by Business Insider, Lansman said the plans would "put Momentum on the proper footing that those dependent on the success of Jeremy's leadership need it to be."
Under the plans, agreed by the group's steering committee, members will have until July this year to become members of the Labour party or leave. The move means several prominent members of the group could face expulsion and was greeted with horror by several leading members on the left of the group.
"I am staggered," Nick Wrack, who was expelled from Labour after standing for the Left Unity party, wrote on Facebook. "It has to rank as one of the most undemocratic manoeuvres in the history of the British left - and that is saying something."
"It has to rank as one of the most undemocratic manoeuvres in the history of the British left - and that is saying something."
Jackie Walker, who was also suspended from the Labour party last year following allegations of antisemitism, described it as "the end of being a social movement."
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Under the changes, anyone who has been expelled from the Labour party will also face expulsion from Momentum.
However, that may not be the end of matter. One senior source within Momentum told Business Insider that expelled members will have the right to have this overturned if the group's national coordinating group decide that their expulsion from Labour was "unfair".
A spokesperson for the Labour party said they have not yet received an application for affiliation from Momentum and the final decision rests with Labour's national executive.
The bid for affiliation is believed to be supported by Jeremy Corbyn. However, it may take some time to complete.
Under current Labour rules, affiliated groups have to supply three years worth of accounts before becoming associated, whereas the group was set up just two years ago.