A Jewish member of Labour’s ruling National Executive Committee has said she is “frustrated” with the pace of action in dealing with allegations of anti-Semitism in the party.

But Rhea Wolfson said she expects the process to speed up with the arrival of new general secretary Jennie Formby, who has been told by party leader Jeremy Corbyn to make the issue her number one priority.

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.

The former Labour MP told The Guardian: “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’. You would be expected to sort out the problem.”

And new NEC member Eddie Izzard told The Mirror: “We must make amends and repair the damage with the Jewish community as Jeremy Corbyn has promised to do.”

Labour has moved to distance itself from a series of pro-Corbyn social media groups after an investigation by The Sunday Times found they contained hundreds of violent and abusive messages.

Mr Corbyn himself deleted his personal Facebook page – although his “official” page remains active.

A party spokesman challenged reports in The Times that more than 17,000 members had left Labour since the start of the year.

“Labour’s membership is well over half a million and in fine health,” said the spokesman. “The latest data have been misrepresented in this story.”

Mr Corbyn is facing demands to speed up the investigations into a backlog of around 70 complaints of anti-Semitism – including one against Ken Livingstone.

Ms Wolfson, who represents constituency Labour parties on the NEC, told BBC Radio 4’s Today programme: “Action has been taken. I am frustrated by the pace of action, as I know a lot of people are – there is a heck of a lot more that needs to be done – but things have happened.

“Restructuring processes have happened, cases have been speeded up, we have brought in more staff, we have set up sub-committees and working groups, particularly on the issue of anti-Semitism, and passed a very important rule change which dealt with a lot of the recommendations of the Chakrabarti report.”

Ms Wolfson said she expected the process to enter a “new stage” as Ms Formby takes the reins of the NEC.

“Jeremy has specifically asked her to make this her number one priority,” she said. “She starts on Tuesday, so I think we will see a speeding up of these changes.”

Ms Wolfson said it was clear that some people within the party were not clear about the dividing line between criticising the state of Israel and straying into “anti-Semitic tropes”.

“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,” she said.

Veteran Labour frontbencher Stephen Pound suggested allegations were being used by Mr Corbyn’s opponents to attack his leadership.

The shadow Northern Ireland minister told Radio 4’s Westminster Hour: “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.”

Mr Pound said Labour should “deal with this our way”, rather than comply immediately with “people screaming from the outside saying, ‘Sling this person out, chuck that person out’.”

“We will take care of this,” he said. “We will clean up this mess because we are the Labour Party, we are not an anti-Semitic party, we’re not a racist party. We’re a party for everyone.”