Jeremy Corbyn has set out new plans to ramp up the expulsion of antisemites from the Labour party at an emergency shadow cabinet meeting, though MPs later angrily questioned why the proposal did not have detail on independent oversight as demanded by senior MPs.

The proposals, which were backed by the shadow cabinet, came before a restive meeting of MPs on Monday night, where MPs including Yvette Cooper and Peter Kyle called on the Labour leader to reflect on why antisemites might be attracted to join the party.

Corbyn told the shadow cabinet before a crunch meeting of the party’s ruling body on Tuesday that a new rule would refer members who had clearly committed the most egregious offences to a new panel of officials, including the general secretary, with the power to immediately expel them.

Presenting the proposals, Corbyn had the backing of key allies including shadow chancellor John McDonnell, who has at times in recent weeks appeared frustrated at the handling of the issue.

Some of Corbyn’s supporters regard antisemitism as a “wedge” issue used to undermine him, and had begun to fear an imminent leadership challenge. But a newfound unity on Brexit, as well as the fresh action on antisemitism, appear to make that unlikely.

However, the Labour leader faced some rearguard action in the meeting from shadow ministers who wanted to beef-up independent involvement in the complaints process, which was not part of Corbyn’s original proposal.

In a joint statement, the shadow cabinet backed Corbyn’s plan but said it also “supports the proposal to introduce independent oversight of our processes”. Corbyn is likely to suggest that could include independent legal advice – stopping short of outsourcing the process entirely.

At the meeting of Labour MPs on Monday night, Corbyn faced an hour of strained questioning from MPs. “It was one of the most tense it has been,” one MP said. “The trust has just gone. And this happens every week.”

MPs said Cooper had berated the Labour leader for the treatment of whistleblowers who spoke to BBC Panorama’s documentary about the crisis, saying they had been smeared and that treated incited more members to verbally attack MPs locally.

Kyle reeled off a list of antisemitic incidents in his Hove constituency, including a member who had proposed a protest march against the local synagogue. “He asked [Corbyn] to consider what it is about his world view – separate from a political platform – that has attracted these people into our party in the first place,” one MP said.

The Jewish Labour Movement also expressed scepticism of the new plan and said it would be handing power to another factional body. “The national executive committee (NEC) is elected on factional slates on the basis of political patronage. It has an in-built majority for the left which does what the leadership of the party tells it to,” JLM’s chair, Mike Katz, said.

“Nothing short of a fully independent process, first asked for by the Jewish community way back in April 2018, is even going to begin to suggest that the party leadership really cares about tackling institutional anti-Jewish racism.”

Labour released new figures on Monday, briefed by the general secretary, Jennie Formby, to the shadow cabinet, revealing it had referred 97 members to the national constitutional committee (NCC), the party’s highest disciplinary body, for possible expulsion since January, with an additional 41 given warnings and 49 given reminders of conduct.

The party said there had been complaints against 625 Labour members, some receiving multiple complaints, but the party had also received complaints about 658 people who were not current members.

However, the figures also suggested that just 28 of those cases had been dealt with by the NCC, resulting in eight expulsions, three suspensions, four warnings and one not guilty finding. Twelve of those referred to the NCC had left the party of their own accord. The equivalent period in 2018 saw just 10 cases heard and seven expulsions – just one fewer than the current year.

Speaking in shadow cabinet, Corbyn said complaints had often taken too long to deal with. “This is not good enough,” he said. “Our members don’t want to share their party with anyone who is racist – and they want to be able to demonstrate there is no place for antisemitism among them.

“Some of the hate and bigotry displayed on social media would count as gross misconduct in any workplace and must be treated similarly robustly in the Labour party.”

Several NEC members, including the party’s deputy leader Tom Watson, proposed changes last week to install an independent appointee with the power to automatically expel members for racism, antisemitism, homophobia, sexism or transphobia.

The change proposed by Corbyn on Monday would not give that independent oversight but would cut out the need to refer members to the NCC where hearings can take months, sometimes years, to take place.

A Labour source said there were significant obstacles to fully outsourcing the disciplinary process. “No other political party or trade union has outsourced its complaints process,” the source said.

“It is unclear how it could logistically work and comply with our responsibilities under data protection legislation..”

Corbyn’s preferred plan would mean those offences that met the criteria would instead be referred swiftly to a special panel including the general secretary and NEC officers – its most senior officials. Both Corbyn and Watson are themselves officers on the NEC, but a party source said they would not be on the panel.

Earlier, Labour peers decided to halt a proposed no-confidence vote in the Labour leader, but sources in the Lords said they could resurrect the plan in September.