Allegations of anti-Semitism within Britain's main opposition party have grown since Jeremy Corbyn, a longtime critic of Israeli actions against the Palestinians, was elected leader in 2015.
While friction between Jewish advocacy groups and Corbyn has existed nearly since the start of his reign, the latest confrontation began when a 6-year-old Facebook posting was brought to public attention last month by a Labour Party lawmaker who is Jewish.
The investigation, the result of two months of research by the newspaper, also found that twelve senior staff working for the Labour leader and the shadow chancellor John McDonnell are members of the groups.
"It has no place in our party", Mr Izzard said.
It is expected that under party rules her seat will now go to comedian Eddie Izzard - the next next most popular candidate at the last NEC election - although party sources said they would have to account of the gender balance of the committee.
The chairman of the All-Party Parliamentary Group against Antisemitism, John Mann, said the tweet was libellous and Lord Sugar "might find it sensible to reword or remove it".
The Sunday Times reported to have uncovered more than 2,000 messages in the groups, which numbered 400,000 members, including anti-Semitism and mysogyny, as well as threats of violence and Holocaust denial. Some were then transferred to a party court, which allowed members legal representation.
"I recognise the hurt that's felt within the community and that's why I responded immediately with an invitation to the Jewish Leadership Council and the Board of Deputies to come and meet me".
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He said the party, which he has donated £1.5m to since 2003, "no longer exists" as he watched the current handling of the anti-Semitism crisis with "growing dismay and foreboding".
One post on a Facebook group called Jeremy Corbyn True Socialism said of Berger, "Get rid of this cancer", while another called her "a vile Zionist".
The image shows the Labour leader's head superimposed on the body of someone sitting beside the former Nazi Party leader.
He said the issue had to be dealt with "for the good of the people Labour seeks to represent".
"It is fine when you hear two or three cases a year".
Sugar was famously a Labour supporter during the Tony Blair years but has distanced himself from the party since Corbyn became leader.
Corbyn had been enjoying a relative lull after an nearly constant media spotlight on cases of alleged anti-Semitism within Labour's ranks through 2016 and 2017.