Momentum’s former vice-chair Jackie Walker has been formally referred to Labour’s highest disciplinary body for possible expulsion over comments she made about Holocaust Memorial Day.

Labour’s national executive committee (NEC) also referred several other members who had been suspended from the party over the summer. Among those were: Paul Davis, the vice-chair of the local party in Wallasey, who was referred over allegations of bullying and intimidation during the leadership challenge by local MP Angela Eagle; and Marc Wadsworth, a party activist who, at the launch of a report into Labour and antisemitism, challenged Jewish Labour MP Ruth Smeeth that she was working “hand in hand” with the media.

Wadsworth said he had not known Smeeth was Jewish and had not intended to offend her at the event.

All three will have their cases heard by Labour’s national constitutional committee, a quasi-judicial body which has the power to expel members from the party. People subject to the proceedings are allowed a defence barrister and all evidence is disclosed to both sides in the case. The committee must rule that offences have been committed “beyond reasonable doubt”.

The NEC held its disputes panel in London on Tuesday to consider the cases, and decided the allegations were serious enough to merit referral to the NCC.

Walker was suspended by Labour in September after she questioned why Holocaust Memorial Day did not recognise other genocides, even though the day is set up to commemorate other atrocities, including those in Rwanda and Bosnia.

After the video of her comments at a Labour conference training event appeared in the media, Walker said whoever leaked the footage “had malicious intent”, and that she was anti-Zionist, not antisemitic.

Walker, who was removed from her position in Momentum, also said she was concerned about definitions of antisemitism used by the party, saying she had not seen a definition she could “work with”.

The long-time activist had previously been suspended from the party after she wrote on Facebook that Jewish people had been “the chief financiers of the sugar and slave trade”. She was later reinstated.

Davis had challenged Eagle to take a lie detector test after the MP said homophobic abuse had been heard at a meeting of the local constituency Labour party during the leadership crisis over the summer. He denied allegations of bullying and intimidation in the Wallasey CLP, which was also suspended.

During the fraught contest, a brick was thrown through the window of a building housing Eagle’s constituency office.

On Tuesday, the NEC agreed steps would be taken to help lift Wallasey CLP’s suspension. New elections would be held for positions in the local party and all new officers would have to undergo equalities training and sign a pledge to abide by Labour party values. Meetings will be supervised by regional officers, and will only be permitted after the elections in May.

A spokesperson for Eagle said the MP had represented the area for 25 years, joining the local Labour party when she was 16. “In all that time she has fought for Labour values and for Labour to be in power,” he said.

“We cannot do that without effective campaigning CLPs that get behind their representatives in the council and in parliament. It is a matter of regret that Wallasey became a site of conflict. Angela takes no pleasure from any individual being referred to the party’s national constitutional committee.”

Eagle’s spokesman said the charges against local members were “exceptionally serious and include witness intimidation, bullying and impugning the integrity of vulnerable witnesses.”

The local party should now focus on fighting the Tories, the spokesman said, with the mayoral election in May and the possibility of a snap general election. “Angela will continue fighting the Tories’ cruel austerity, their strategy for Brexit that puts at risk local jobs and livelihoods and to defend our local NHS which is being threatened with £1bn in cuts,” the spokesman said.

Ken Livingstone, the former mayor of London who was suspended last summer for comments that Adolf Hitler had been a Zionist, was referred to the NCC earlier this year. A hearing has yet to take place.

• This article was amended on 8 March 2017 to expand a quotation.