Labour's election defeat was repeatedly blamed on the media, the party's unsupportive MPs and the dominance of Brexit as an issue.
The audience - who included Gordon Nardell QC, who failed to win the City of Westminster seat for Labour - were urged to back Ms Long-Bailey to carry on Mr Corbyn's "socialist anti-austerity project".
Ms Webbe, a former member of Labour's ruling NEC body, who was elected to the safe Leicester East seat, said Labour would not win the next election by "rolling back on Jeremy Corbyn's anti-austerity agenda."
She added Ms Long-Bailey was "right" to suggest that Labour’s defeat wasn’t because of the party's policies.
"Rebecca Long-Bailey gets it," said Ms Webbe.
But as the event organisers awaited the arrival of Mr Burgon, who is standing to be the party’s next deputy leader, activists were asked to speak from the floor.
Brent Central's Mr Durham, a former school teacher and member of the Unite trade union, was first to take to the microphone.
He told the meeting: "I don't think we should just be appointing people because they supported Jeremy Corbyn."
Then, in a reference to Labour members who were suspended or expelled over alleged antisemitism, he asked of Ms Long-Bailey: "Does she oppose the vicious witch-hunt of good socialists in the Labour Party?"
Mr Durham then added: "She has been cuddling up to the Jewish Labour Movement and the Chief Rabbi, a well-known Tory. We should not be allowing that."
While some in the audience cheered, two people stood up and walked out of the room shouting: "You are an antisemite!"
But Mr Durham continued: "We are in favour of people expressing their views on Israel as much as they feel they need to, as we saw at Labour Party conference.
"You do not spend your time cuddling up to the Chief Rabbi."
The meeting was chaired by Emina Ibrahim, a leading Haringey Momentum figure, who did immediately intervene and instruct another official to remove the microphone from Mr Durham.
But Ms Webbe, who was seated on the stage at the time of the incident, remained silent and took no steps to counter the comments.
Asked to comment on Mr Durham's remarks by the JC, Ms Webbe did not respond.
Mr Burgon, who arrived at the venue after the comments were made, later said he was "disturbed" by the outburst and added that he would "condemn racism in all its forms."
The JC also approached David Rosenberg and Julia Bard, from the Jewish Socialists Group, who had been seated near the front of the venue, to ask for their view of Mr Durham's remarks.
Neither issued any condemnation.
In his speech, Mr Burgon said last month's election results were "devastating" for Labour - but he did not blame Mr Corbyn for the loss.
He said he was "proud" to back Ms Long-Bailey to become new Labour leader.
Speaking earlier, Councillor Pamela Fitzpatrick, who failed to unseat Conservative MP Bob Blackman as Labour's Harrow East parliamentary candidate, said: "Our policies were not unpopular."
She accused fellow Labour councillors of secretly being pleased Mr Corbyn was defeated on election night at the count in Harrow.
Ms Fitzpatrick also attacked suspensions from the party as she too backed Ms Long-Bailey.
The JC contacted Mr Durham to comment further on his remarks about Chief Rabbi Mirvis and the JLM at the meeting but he did not reply.
