Up to 40 MPs are understood to be considering their futures in the party if Ms Long-Bailey is named as the next leader, which could see some sit as independents or some leave politics.
Ms Long-Bailey, the shadow business secretary, is one of the favourites to win the leadership contest, with her shadow cabinet colleague Sir Keir Starmer emerging as her main rival.
A close ally of Mr Corbyn, Ms Long-Bailey is regarded as the left-wing successor to the Labour leader, although she has repeatedly rejected claims that she is merely a "continuity" candidate.
She alarmed some moderates in the party with her support for open selections - a process which makes it easier for local branches to deselect their MP.
The Salford and Eccles MP also sparked concern when she gave Mr Corbyn a 10/10 rating for his performance as leader - despite the party's election drubbing and the long-running row over handling of antisemitism complaints.
One MP told The Independent: "Some of us have been talking about walking out for some time. Between 30 or 40 MPs.
"I would sit as an independent."
Concerned MPs are understood to be discussing their options in WhatsApp groups rather than meeting formally as a bloc.
Bermondsey and Old Southwark MP Neil Coyle, who put the number “closer to a dozen”, told HuffPost UK: “Continuity Corbyn is a death knell for Labour.
“Division, factionalism and introspection will continue. Favouritism and bullying will continue. Antisemitism will continue. Failure in elections will continue.
“More MPs and others will leave. The frontbench will continue to fail to reflect members. It’s a recipe for disaster.”
A spokesperson for Ms Long-Bailey said: "If any candidates are truly serious about uniting or ending factionalism, their campaigns should all want to condemn this sort of nonsense.
"Whoever wins the leadership contest will have a mandate and all members especially MPs should unite behind them to campaign for a Labour government."
It comes as the Labour leadership contest descended into acrimony after Sir Keir's team was accused of hacking into the party's membership databases.
Two members of the shadow Brexit secretary’s team are understood to have been reported to the Information Commissioner's Office by Labour bosses over the row.
Sir Keir's campaign said it is "scurrilous" to suggest they breached data rules, with his vice-chairman David Lammy saying "categorically that this did not happen".
He told the BBC Radio 4's Today programme: "There was no attempt by the campaign to do this - it's scurrilous to suggest so and I'm quite sure that the Information Commissioner will find the allegations completely untrue."
The Labour MP warned against a "scramble to the bottom" but stopped short of blaming a rival campaign for the row.
A spokesperson for Ms Long-Bailey’s campaign: "The investigation into Keir Starmer’s campaign over an alleged data breach should not be allowed to distract from a moment of significant importance in determining the future direction of our party.
"As Rebecca’s campaign has said previously, the accessibility of members’ data stemmed from a failure to close Dialogue at the end of the general election campaign."
The move came after general secretary Jennie Formby launched an investigation into claims Ms Long-Bailey’s campaign had shared links to a Labour phone-banking system with volunteers, potentially allowing them to contact more than half a million party members.
Her team insist they have done nothing wrong and it is understood that party officials have so far found no evidence to substantiate allegations against them. Suspicions of breaches by the Starmer team are thought to have emerged in the course of this investigation.
The new Labour leader and deputy leader will be announced on 4 April after a vote by party members.
Wigan MP Lisa Nandy has made it onto the ballot paper but Emily Thornberry, the shadow foreign secretary, is struggling to secure enough support to get through to the final round.
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