Labour MPs have claimed the party’s general secretary, Jennie Formby, had “not learned anything” when they confronted her about the handling of antisemitism at a tense meeting in Westminster on Monday.

Formby faced a coordinated onslaught from MPs, who challenged her over a report in Sunday’s Observer that members of Jeremy Corbyn’s inner circle had taken a direct role in sifting out some disciplinary cases. She told MPs that political appointees were no longer given any role in disciplinary cases.

But Louise Ellman, the MP for Liverpool Riverside, who has repeatedly expressed concerns about the party’s record on the issue, emerged from the weekly meeting of the parliamentary Labour party (PLP) to say she felt “angry” about Formby’s responses.

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“She was talking about ‘rightwing antisemitism’. She still said it was a small percentage [of Labour members involved in antisemitism], which is completely beside the point. I don’t think she’s learned anything,” she said. “The problems with the party’s failure to deal with antisemitism are political.” Ellman suggested some senior Labour party figures would “find every reason possible not to discipline someone who is from their group”.

Labour was forced to deny last week that Corbyn had been directly involved in the initial decision not to suspend the Derby North MP and close ally Chris Williamson while a “pattern of behaviour” was investigated.

Williamson was caught on film saying Labour had been “too apologetic” over antisemitism. Formby eventually reversed the party’s initial decision and suspended him after several hours of intense lobbying from inside the party.

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Another MP said Formby had taken what he called a “hammering” and suggested there was a “complete breakdown in trust” in the party’s most senior official.

However, a Labour party source said: “Jennie set out her commitment to increasing transparency, ensuring constituency Labour party meetings are respectful and comradely and that all Jewish people feel welcome in the party. She reiterated her offer to meet any members of the PLP individually or in small groups to discuss their concerns and hear their ideas about further improvements to procedures.”

Ellman said the Jewish Labour Movement would discuss on Wednesday whether it could continue to remain affiliated to the Labour party, although no final decision would be taken.

Her fellow Liverpool MP Luciana Berger cited antisemitism as the key motivation for her decision to quit the Labour party and join the breakaway Independent Group last month. Since then, Formby has come under intense pressure to step up the party’s response.

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Veteran Labour MP Margaret Hodge said MPs had asked the general secretary about the party’s response to motions passed by several constituency Labour parties in support of Williamson. “She talked vaguely about sending letters or a bit of training but, if we’re serious about antisemitism, you expect action,” she said.

Labour is yet to confirm formally that it has appointed Lord Falconer to carry out an independent review of how the party investigates antisemitism cases. His appointment was cited as a positive move by the shadow chancellor, John McDonnell, at the weekend, but no terms of reference have yet been announced and some party insiders claimed on Monday that Falconer had caused disquiet by demanding access to historical emails and servers.

That was denied by a Labour source, however, who insisted: “Jennie said Charlie will have access to whatever he needs. She’s always made that clear; there hasn’t been disagreement on that.”

Falconer attended Monday’s meeting and was asked as he left whether he had been appointed. “Not yet,” he replied.

Formby was involved in a public spat with Labour’s deputy leader, Tom Watson, on Friday after she copied the party’s parliamentarians into a strongly worded letter rebuking him for asking MPs to copy him into antisemitism complaints and saying he risked “polluting” the existing complaints process and breaching data protection rules.

She was also questioned on Monday about reports that Laura Murray, who is Corbyn’s stakeholder manager, had been seconded to Labour’s complaints unit.

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The Stoke MP Ruth Smeeth called the temporary appointment “extraordinary”, but a Labour source insisted Murray had close and constructive relationships with Jewish groups and said two members of staff had been temporarily seconded to the complaints unit from other parts of the organisation to provide administrative support with recent complaints. A spokesman said: “We do not comment on staffing matters.”