Former Home Secretary Alan Johnson, who ran Labour's campaign for a Remain vote in the referendum, claimed the leader's office had "conflicting objectives" to the rest of the party.
Corbyn's grip on the Labour leadership looked increasingly weak as business spokeswoman Angela Eagle became the most senior member of his shadow cabinet to quit.
He was heckled by his own side in the House of Commons with calls of "resign" from behind him in his backbenches.
Shadow housing minister John Healey, shadow energy secretary Lisa Nandy and shadow work and pensions secretary Owen Smith have all resigned - adding to the 12 shadow cabinet members Corbyn lost yesterday.
Sources said that Corbyn will refuse to step down and will instead try and make public the planned secret vote on his future so that voters can see which MPs are trying to unseat him.
Corbyn has been forced to promote a number of key allies as the revolt against his leadership intesnifies.
A number of the 2015 intake have joined the new shadow cabinet with just a year's experience on the job.
Corbyn faced a "hostile" meeting with Labour MPs and peers who told him he must quit for the sake of the party.
Many MPs appeared close to tears after a volatile meeting that former leadership contender Chuka Umunna described as "pretty catastrophic".
Yesterday Corbyn issued a bullish statement and vowed to continue as leader despite the resignations. He said: "I am not going to betray the trust of those who voted for me - or the millions of supporters across the country who need Labour to represent them.
"Those who want to change Labour's leadership will have to stand in a democratic election, in which I will be a candidate.
"Over the next 24 hours I will reshape my shadow cabinet and announce a new leadership team to take forward Labour's campaign for a fairer Britain - and to get the best deal with Europe for our people."
- additional reporting PA
