The political party he once supported "no longer exists", said Garrard, according to The Guardian.
In a Passover message on Friday, Mr Corbyn said it was easy to denounce anti-Semitism overseas but sometimes harder to see it closer to home.
If Labour were elected to govern, Abbott would serve in Corbyn's cabinet as Home Secretary, a position which would put her in charge of hate crime, including anti-Semitism.
It comes after 39 Labour MPs and peers signed a letter to Mr Corbyn on Thursday evening in which they urged him to oust Ms Shawcroft from the National Executive Committee and suspend her party membership.
Ex-Commons Speaker Lord Martin called for a special one-day conference of members to address the problem and demonstrate the party's abhorrence of anti-Semitism.
"If you ran a restaurant, and it was dirty and there were cockroaches, you wouldn't get away with saying "the restaurant down the road is dirty and has cockroaches too".
Christine Shawcroft, a leading Corbyn ally, quit her role as chair of Labour's disputes panel on Thursday after admitting she was "wrong and misguided" to have sent an email calling for a Peterborough council candidate to have his suspension lifted.
Momentum's NCG believes that accusations of antisemitism should not and can not be dismissed simply as right wing smears nor as the result of conspiracies.
The move came as the Labour leader promised "watertight" investigations into allegations of anti-Semitism. "We're a party for everyone".
"But this issue is not about individuals or party groups; it is about a rotten culture that is growing in Labour that must be rooted out".
While Mr Corbyn's opponents were "opportunistically using this issue as a way to undermine his leadership", this did not reduce the need to challenge anti-Semitism, the statement said.
In an open letter to Mr Corbyn, they said: "It is utterly wrong that somebody who defends a Labour candidate who has been suspended for Holocaust denial should be a member of Labour's governing body".
Ms Wolfson told the BBC's Today programme: "There is very clearly a real issue, a huge piece of work that needs to be done in the Labour Party, around modern anti-semitism and giving people the tools to recognise when legitimate criticism of Israel crosses the line into anti-semitism". He added: "A few people were angry with how she spoke in the meeting".
"I think the Labour Party without a doubt has a problem, but on the other hand there are some people who are riding that horse to attack Jeremy Corbyn anyway".
"Jeremy has specifically asked her to make this her number one priority", she said.