A Labour peer has said the party has a “serious problem” with anti-semitism, following yesterday’s suspension of Naz Shah – while some Labour figures have prompted dismay by claiming the Bradford MP has not made any anti-semitics remarks.

Lord Levy, who served as Tony Blair’s personal envoy to the Middle East, said last night that while “every party” needs to address the issue of anti-semitism, it is currently “more prominent within the Labour Party”, and said that the leadership had “dithered” in dealing with the case of Naz Shah.

However, former London Mayor Ken Livingstone and Ealing Central MP Rupa Huq have both played down accusations of anti-semitism against Shah, with Huq this morning telling the Today programme that her actions had been “silly”.

Appearing on Newsnight last night, Levy said that “there are definite issues of anti-semitism across the political spectrum. At this moment in time, I have to say it seems more prominent within the Labour Party. And it’s absolutely crucial that the leadership stamps this out once and for all.”

Levy, who has been a Labour peer since 1997, said that the party leadership “taken too long” to suspend Shah from the party after her social media posts emerged on Monday morning. “Somehow they dithered at the beginning,” he said.

And he added that the party must take a more “proactive” approach to rooting out anti-semitism, saying that “members of the party and anyone associated with the Labour Party coming out with this sort of anti-semitic verbiage and really disgusting posts cannot be tolerated.”

“Every party needs to look in the cupboards at what is going on with anti-semitism at the moment,” he added.

The Jewish Labour Movement last night issued a statement saying that Naz Shah’s comments had been “repugnant and completely unacceptable”, but welcomed that “her contrition expressed over the past day seems to be genuine and sincere.”

But Ken Livingstone said that he had “never heard” anti-semitism in the Labour Party during his decades of membership, and seemed to suggest that the problem was being exaggerated.

“What we have at the moment is a lot of people making a big issue about anti-semitism in the Labour Party. In 47 years I have never heard anyone say anything anti-semitic,” Livingstone told LBC.

“We expelled a couple of people from the Labour Party early on for saying things that could clearly be interpreted as anti-semitic,” he said, adding that in Shah’s case “this is not that.”

“This is an over-the-top comment about the horrendous conflict between the Israelis and the Palestinians.”

Speaking this morning, Rupa Huq said that Shah had been silly, and was guilty of sharing offensive posts on social media rather than making the comments herself. “She did not write anything anti-semitic, she just pressed share,” Huq said.