Labour's deputy leader Tom Watson has said he "deplored" his party's response to claims that some of Jeremy Corbyn's closest allies tried to interfere in disciplinary processes involving allegations of anti-Semitism.
Labour has insisted the claims in Wednesday's Panorama were inaccurate and made by "disaffected" former staff.
But Mr Watson said dismissing the testimony of the staff was "wrong".
And Chief Rabbi Ephraim Mirvis said the leadership was "directly complicit".
But shadow chancellor John McDonnell said the "serious charges" were being "hotly contested", and the process of dealing with complaints in the party had been "improved dramatically".
Labour's disputes team is supposed to operate independently from the party's political structures, including the leader's office.
BBC Panorama spoke to former party officials, who alleged they had to deal with a huge increase in anti-Semitism complaints since Mr Corbyn became Labour leader in 2015.
Some of the staff spoke to the programme despite having signed non-disclosure agreements (NDAs) when they left.
Eight former officials who worked in the team and dealt with anti-Semitism cases claimed to the BBC that:
- The leader's office was "angry and obstructive" when it came to the issue
- Officials brought in by the party's general secretary, Jennie Formby, "overruled" some of their disciplinary decisions and "downgraded" punishments to a "slap on the wrist"
- Seumas Milne, one of Mr Corbyn's closest aides, laughed when advised by a long-serving party official about what Mr Corbyn should do to tackle anti-Semitism in the party
- On one occasion, Mr Corbyn's office ordered batches of anti-Semitism complaints to be brought to his Commons office for processing by his aides
Labour has rejected claims of interference and described the programme as "seriously inaccurate" and "politically one-sided".
Mr McDonnell - a close ally of Mr Corbyn - said current staff had put in complaints to the BBC about the accusations made in the Panorama programme.
"I have always said from the very beginning [the process of dealing with complaints] was too slow and not ruthless enough, but it has improved dramatically now," he said.
"I think it is important that we listen to what has been said and look ourselves at what is happening, but what we've got now is two groups of staff challenging the accuracy of [the accusations] so we will have to look at that."
But Labour's shadow women and equalities minister Dawn Butler - who is a supporter of Mr Corbyn - said the party "must acknowledge the deep hurt caused to our Jewish brothers and sisters".
I watched the BBC’s panorama programme last night and was saddened, we must acknowledge the deep hurt caused to our Jewish brothers and sisters by anti-Semitism within the Labour family. We must build bridges and fight racism together.#Panorama pic.twitter.com/tJsCo8IWtC— (((Dawn Butler MP))) (@DawnButlerBrent) July 11, 2019
Three Labour MPs - Ruth Smeeth, Margaret Hodge and Louise Ellman - have written to Mr Corbyn, saying there is "no justifiable reason for your continuing failure to act".
They added: "The ongoing inaction and tolerance of anti-Semitism has made a mockery of the party's core values of anti-racism and promoting equality. By ignoring this issue, you are turning a blind eye to anti-Jewish racism in the party".
Mr Watson told BBC Radio 4's Today programme the party needed new measures to tackle anti-Semitism - including automatic expulsion of members.
"In the last four years since Jeremy and I were elected leader and deputy leader of the party, there is a growing belief that there is a sickness in our party, that this kind of abuse has been in some way allowed, that there is almost a permissive culture that people can use anti-Jewish racist language... that we have failed to address adequately," he said.
Asked if he thought Mr Corbyn had what it takes to fix the party, Mr Watson said: "Not only do I think he can fix it, I think he is the only one who can fix it."
He added: "I am not going to turn a blind eye to anti-Jewish racism. I am going to call it out, day in, day out, until action is taken.
"That might cause great difficulty for my colleagues in the shadow cabinet who are also collectively responsible for this, but until we have dealt with it, until we have actually changed our rules, until we have actually attacked the culture at its root cause, then I am not going to resile."
Chief Rabbi Mirvis tweeted a statement after Panorama aired, saying the programme "must be a watershed moment in this agonising saga".
He added: "This is no longer a question of the leadership's inability to deal with the scourge of anti-Semitism, but of its direct complicity in it.
"The cloud of hatred and acrimony that this creates must be lifted from our politics and from our society.
"Quite simply, we cannot go on like this."
In May, the Equality and Human Rights Commission (EHRC) launched a formal investigation to look into whether Labour had "unlawfully discriminated against, harassed or victimised people because they are Jewish".
The Jewish Labour Movement said on Thursday that more than 30 whistleblowers, including current Labour staff, would submit evidence to the inquiry.
Other MPs and peers in the party also offered their support to the former staff in the Panorama documentary, adding that it showed Labour was failing to effectively tackle anti-Semitism in its ranks.
Labour peer Lord Falconer said the leadership had to "change gear" over the issue.
Fellow Labour peer Lord Levy, a former party fundraiser under ex-PM Tony Blair and a leading voice in the British Jewish community, said the party should feel ashamed of what was going on.
The Board of Deputies of British Jews said the Panorama programme added weight to the group's suspicion that the issue of anti-Semitism had been "treated with disdain".
Labour has been engulfed in a long-running dispute over anti-Semitism within its ranks, which has led nine MPs and three peers to leave the party.
The leadership has been accused of failing to get to grips with the problem, with allegations of hundreds of complaints against members remaining unresolved.
But Labour said it "completely" rejected any claims it was anti-Semitic.
It accused the Panorama programme of being a "seriously inaccurate, politically one-sided polemic, which breached basic journalistic standards, invented quotes and edited emails to change their meaning".
The party said that "no proper and serious attempt was made to understand our current procedures for dealing with anti-Semitism, which is clearly essential to reach a fair and balanced judgement".
It added: "Since Jennie Formby became general secretary the rate at which anti-Semitism cases have been dealt with has increased more than fourfold.
"We will build on the improvements to our procedures made under Jennie Formby, and continue to act against this repugnant form of racism."