Labour’s former head of disputes Mike Creighton also attacked the new plans writing: "So it seems that any possibility of an Independent Complaints Procedure has been scuppered by LOTO (leader of the opposition) at today's NEC.
“The disciplinary procedure is now fully factionalised as Corbyn ensures control of the final lever of power in the Labour Party.”
Some MPs are angry that a separate plan for a fully independent disciplinary process was not adopted.
Deputy leader Tom Watson withdrew a motion calling for the Bar Council, or another similar legal body, to appoint an independent person to devise a new complaints scheme.
He backed down after it was clear the motion would not pass, as the NEC is now dominated by pro-Corbyn members.
A Labour source said the party would now bring forward proposals for "independent oversight" of its processes to increase transparency, without giving any further details.
In a joint statement, the Board of Deputies and the Jewish Leadership Council said: "Jeremy Corbyn’s proposals on antisemitism, presented to the Shadow Cabinet, represent a significant step backward.
"The proposals significantly increase the potential for political interference by putting decisions further into the hands of a small group of individuals who consistently vote on factional lines and have already shown their lack of independent thinking.
“The party seems intent on preserving a system that primarily protects antisemites at the expense of their victims.
"Once again, the Labour leadership refuses to make the disciplinary process independent or transparent, despite being repeatedly asked to by our community and by victims of other complaints.
“We urge Labour to get serious, stop presuming they understand antisemitism better than the Jewish community and adopt a robust system based on the recommendations set out by Jewish community organisations and others.
"Only then will they begin to rid themselves of this racism.”