John McDonnell has said Labour needs to “sit up and listen” to complaints about antisemitism in the party, as a senior Jewish MP called for more action to tackle the problem.

The shadow chancellor pledged that the party would root out antisemitism after a series of scandals involving activists and some councillors making offensive comments about Jewish people.

The latest involved the suspension of Khadim Hussain, a Labour councillor and former lord mayor of Bradford, who was put under investigation for sharing a Facebook post that said “your school education system only tells you about Anne Frank and the six million Zionists that were killed by Hitler”. He has now quit the party.

Labour has repeatedly said there is no place for antisemitism in the party and launched a number of investigations into the conduct of individuals. However, Louise Ellman, one of Labour’s most senior Jewish MPs, said on Sunday there had not been enough action to tackle the problem

Speaking on Sky News’s Murnaghan, she said: “I am very concerned about antisemitism in the Labour party. Most members of the Labour party are not antisemitic but some are and some are being allowed to get away with posting antisemitic comments in their tweets and on their websites.

Louise Ellman said Labour needs to do more to tackle antisemitism. Photograph: John Stillwell/PA

“I have raised this in parliamentary meetings and the leader has spoken out clearly. He says that he is against antisemitism. But it is not just about words. There has got to be some action and we haven’t seen enough of that.”

McDonnell, who said last week he wanted those with antisemitic views to be expelled from Labour, said in an interview on the BBC’s Andrew Marr Show on Sunday: “As soon as Jewish people start telling us there is antisemitism in our party, we’ve got to sit up and listen.

“That is why I said last week, if there are people who have expressed antisemitic views, there is no role for them in our party and I would like them out of our party for life. I believe we should take the advice of the British Board of Deputies and our other Jewish friends and say how shall we tackle this problem. It is a societal problem. If it has infected any of our Labour party, we have got to root it out and I am not having it within our party.”

Asked about the case of a former Labour parliamentary candidate, Vicki Kirby, who was readmitted after being suspended over offensive comments about Jews, McDonnell said: “That is unacceptable. You can be a critic of the Israeli state but you must not allow that in any way to be used by antisemites. You’ve got to root that out and we will.”

Several other senior figures in the party have called for more action on the issue. Lord Levy, who was Labour’s chief fundraiser under Tony Blair, warned he may quit the party if it did not do more to confront anti-semitism. Chris Bryant, the shadow leader of the House of Commons, has said the issue of antisemitism threatened to destroy Labour values.