The shadow Brexit secretary, Keir Starmer, has called for tough rules to swiftly kick out antisemitic Labour members, following rows at a shadow cabinet meeting over the party’s backlog of complaints.

The deputy leader, Tom Watson, clashed with the party’s chair, Ian Lavery, at a shadow cabinet meeting on Tuesday which was entirely dedicated to the subject.

Watson accused the Liverpool Wavertree branch of “bullying” its MP, Luciana Berger, who has also been subjected to antisemitic abuse. Lavery criticised Watson for calling for the branch to be suspended, sources said.

Labour’s general secretary, Jennie Formby, revealed on Monday that 673 complaints alleging antisemitism against party members had been made in the past 10 months, resulting in 12 expulsions.

Some Labour MPs including Dame Margaret Hodge said the figures could not be trusted. Hodge, the former chair of the public accounts committee, said she had submitted 200 examples of alleged antisemitism.

Questioned on BBC Radio 4’s Today programme about the meeting, Starmer said: “There was a real sense of frustration, shared by myself, that however much the processes have changed, there needs to be a way in the Labour party in clear cases to take swift action and deal with people. If they need to be expelled in clear cases, then that should happen.”

Starmer added that the Wavertree Labour party branch should not be suspended.

Also questioned about Brexit, Starmer said the option of a second referendum remained on the table for Labour.

“In reality, for the Labour party,” he said, “the only credible options now left are a close economic relationship – that’s the sort of relationship we spelled out in the letter to the prime minister last week – or a public vote.”

He declined to comment on reports that claimed the leader’s office removed a reference to a referendum from Corbyn’s letter to the prime minister.

“The letter set out the close economic relationship in detail, it was credible, it’s been well received in the UK and the EU,” he said.

Starmer said Labour would also support the amendment put forward by his fellow Labour MP Yvette Cooper, which would force the prime minister to put the choice of no deal or an article 50 extension to the Commons if she has not signed a deal by the middle of March.

“We will support that,” he said. “The sense that this can’t be allowed to go on is growing.”

But he sidestepped the question of whether frontbenchers who failed to vote for the Cooper amendment would be sacked, saying: “The job of deciding what people do on the whip is the chief whip’s job, along with Jeremy Corbyn.”