At last Sunday’s Board plenary meeting, President Marie van der Zyl told deputies the organisation “would lose all our power” if they “were to stop engaging with Labour.”
She added: “Suspending relations with the party may create headlines but it would get us nowhere and leave us no wriggle room.
“I have always said that engagement does not mean concessions.”
Senior Liberal Judaism Rabbi Danny Rich has said the community had “an obligation to work very closely” with Labour and said he feared the community’s leaders could be “in danger of being accused of only desiring regime change” in the party.
Rabbi Rich recently hosted a Shabbat dinner with Mr Corbyn, the co-chair of the Jewish Voice For Labour group Jenny Manson and their partners.
But Dame Margaret, who told Mr Corbyn to his face in the House of Commons that he was "antisemitic", told the JC on Wednesday: “He is the leader of the leader of the Labour Party. The onus is on him to take the first steps and try and rebuild the relationship.
"There is no way you can compromise on antisemitism.
“I don’t understand what a compromise would look like. When I was having the argument, they kept saying, ‘will you apologise?’ and I wouldn’t.
“He’s the leader. He has got to take the first steps. He created this situation. He is the architect of where we are now.
“He has to be the leader in trying to break the deadlock.”
The JC has learned that other Labour MPs – Jewish and non-Jewish - who have faced the full brunt of antisemitic attacks from within the party have been left “angry and confused” by calls for engagement with the leadership.
They stress that there has been no compromise from Labour's leaders since the Enough Is Enough demonstration in Parliament Square in March.
The party has not heeded calls by the Board of Deputies, the Jewish Leadership Council and the Jewish Labour Movement to drop an investigation into the MP Ian Austin for alleged “abusive conduct” after protesting about Jew-hate.
A Board spokesperson told the JC:" We have made a series of clear asks of Mr Corbyn. We want to see action on them and we will continue to push for them until we do.”
