Labour has taken too long to stamp out antisemitism in the party, a key ally of Jeremy Corbyn has said.

The shadow business secretary, Rebecca Long-Bailey, said it was imperative for the party to urgently address the problem to ensure that the Jewish community felt welcome.

In an interview for BBC Radio 4’s Today programme, she said: “Jeremy has always been a militant opponent of antisemitism, but too often the issue has been dismissed as a few bad apples when we need to take very serious root and branch action, to root out the cause of the problem.”

Her comments came after some Labour MPs joined protesters outside parliament following claims from Jewish leaders that Corbyn had become a figurehead for antisemitism.

Corbyn himself conceded that his party had failed to address the problem and issued his strongest apology yet over his 2012 backing of a graffiti artist behind an antisemitic mural.

Long-Bailey, a staunch supporter of Corbyn who is touted as a potential future party leader from the left, said it was “devastating to realise that the Jewish community had lost faith in our approach to antisemitism”.

Lord Levy, Labour’s former chief fundraiser, said he was considering leaving the party over the issue. Asked if he still felt at home in the party, he said: “I’m not sure. I put myself under the microscope continually because the provenance of Corbyn comes from a certain element of the left and they seem to be able to call the shots. If these people are antisemitic [and if] they do not believe in zero tolerance on antisemitism, they should not be part of this Labour party.”

Long-Bailey insisted Labour did take a zero-tolerance approach to antisemitism but this had not been “enforced as effectively as it should have been”.

She also called for faster implementation of recommendations made by Shami Chakrabarti in a report for Labour on allegations of antisemitism.

She said: “There will be clear efforts now to roll out a political education programme specifically to make sure that every single person in the Labour party is aware of all forms of antisemitism ... to make sure nobody suffers in the way that they have done.”

Long-Bailey said she hoped Jewish leaders would help Labour to tackle the issue. “I would really welcome a meeting as urgently as possible between Jeremy and the Board of Deputies and the Jewish Leadership Council because we have to work collaboratively on this,” she said.

On Corbyn’s comments about the mural, she said: “It was clearly an antisemitic mural, and Jeremy has apologised for not looking at it. We are all human unfortunately and it’s a lesson to us all to look clearly at the things we are supporting or commenting on on Facebook.”

Levy was reluctant to accept Corbyn’s apology. He said: “It is all well to say that he didn’t realise what was in it, I just don’t accept that. I think this is a man who does not have sensitivity to understanding where the community comes from and what the Jewish community stands for and believes in.”

On Monday night, the former Labour prime minister Tony Blair said he did not believe Corbyn was antisemitic but said there were people around the leader who “don’t really think this is a serious issue”.

He told BBC Two’s Newsnight: “I think up to now at least they haven’t really got it. I think they would be very wise to listen to what the Jewish community is saying today and act on it.”

Asked why action on the issue had taken so long, he replied: “I don’t know. Because I think there are people, around him at least, that don’t really think this is a serious issue, and hopefully now they realise that it is.”