Labour’s deputy leader, Tom Watson, challenged Jeremy Corbyn directly on Sunday to address what he called “a crisis for the soul of the Labour party” or risk many more defections to the Independent Group.

In a forthright interview on The Andrew Marr Show, Watson urged Corbyn to take personal leadership of efforts to tackle antisemitism in his party and to reach out to MPs from the social democratic tradition.

“My message to our Labour party, to our half million members, is – ‘look, I know we’re in a crisis. The departure of our colleagues is a real blow to us, and we need to understand why they felt they need to go, because if we’re going to be in government, we need to address those concerns’,” he said.

Watson’s intervention was the latest blow in an escalating war of words between Corbyn and his deputy, who is directly elected by party members.

Watson said he had received 50 complaints about antisemitism from colleagues in the past week, which he had forwarded to Corbyn. “Jeremy needs to understand that if we are going to be in No 10, he needs to change the Labour party,” he said. He needs to take a personal lead in reviewing those cases, and recommending to the national executive committee what needs to be done.”

Details of the dossier, seen by the Guardian, include Labour members sending tweets linking Hitler and the Rothschilds, accusing Jews of murdering children and questioning whether Jewish MPs and councillors have “human blood”.

All of the cases have been raised by Watson or other Labour MPs over a period of several months, but no action has been reported back to those who have raised the complaints, he said.

One case involved a tweet, which read: “Wonder why Jewish people are hated wherever they’ve settled over last 2000 years. Their double dealing, back stabbing, cheating chilling coldness has always only one outcome. I wonder what the average period of time is before people fed up with the anti-social Jews kick em out”.

Another concerned a tweet saying that “Jews murder people and children”.

A third complaint involved comments about Jewish MPs and councillors that said: “Don’t know what runs through their veins, not human blood” and “their hearts and brains totally devoid of humanity”. One of those attacked was Liverpool Riverside MP Louise Ellman, who is deemed at risk of following Luciana Berger’s example and quitting the party.

A fourth complaint related to social media posts, including one that said: “Hitler is an illegitimate Rothschild, so any offspring of him who would have a good chance of being propelled into a position of power.”

Watson said Corbyn should review the details of all 50 cases personally, and “go to the NEC, where he is in control. They will back him if he says ‘these people need to be thrown out’”.

Labour sources were quick to play down the idea that Corbyn could take a direct role in examining specific cases, however, stressing that the leadership did not oversee the party’s disciplinary process.

A spokesperson said: “The Labour party takes all complaints of antisemitism extremely seriously and we are committed to challenging and campaigning against it in all its forms. All complaints about antisemitism are investigated in line with our rules and procedures and any appropriate disciplinary action is taken.”

Many MPs have felt frustrated that while Labour’s general secretary, Jennie Formby, has repeatedly promised to step up efforts to tackle antisemitism, specific cases raised have resulted in little or no action. “Very patently, the Jennie Formby reforms have not been adequate. They have not succeeded,” Watson said.

He also reiterated his demand for Corbyn to reshuffle the shadow cabinet to give greater weight to MPs with social democratic rather than socialist views. If that did not happen in the days ahead, he said he would “convene a group of MPs, who believe in that tradition, to develop policies”.

The as-yet-unnamed group, which is expected to meet in the next fortnight, will commission research and draft papers to submit to the shadow cabinet and Labour’s policy forums.

Watson said Labour had always been an amalgam of different traditions. “We’re only electorally successful if those traditions can rub up against each other,” he said. “Harold Wilson had Tony Benn and Roy Jenkins in his cabinet, and so that is our challenge.”

He also lent his support to efforts by the shadow Brexit secretary, Keir Starmer, to persuade the leadership to swing its weight behind a second referendum. “What we would prefer is that Theresa May aligns around our red lines, which is closeness to the EU, but if we can’t get our red lines met, then conference policy, negotiated by Keir Starmer, is that we go for a people’s vote,” he said.

The shadow chancellor, John McDonnell, said on Sunday that Labour was moving toward supporting a referendum, and that the party could back a redrafted version of an amendment suggested by the Labour MPs Peter Kyle and Phil Wilson under which the prime minister would put her deal to a public vote.

“There’s increasingly large numbers of people who will consider now moving towards a public vote situation to block a no deal, and to block a bad deal,” he said.

Watson hit back against Corbyn’s insistence on Friday that there was no place for bullying in the Labour party, repeating his claim that Berger, the Liverpool Wavertree MP who was sitting across from him in the BBC studio, had been “bullied out of the Labour party by a small number of racist thugs”.

Asked about these claims by Sky News on Friday, Corbyn said there was “no place for harshness, bullying or anything else in the party. And to tell you the truth, I don’t believe it exists on a wide scale”.

After seven Labour MPs resigned on Monday, to be followed by another two by the end of the week, Watson urged the Labour leader to “broaden out” the frontbench, to reflect the range of views in the wider parliamentary party.

When Corbyn was asked directly about that demand last week, he shrugged it off. “Anyone who does not feel consulted is not taking up, in my view, the opportunities that are available, at all times, to do that,” he said.

The Labour leader and his close allies have also taken a robust stance against the defectors, urging them to call byelections in their seats.

The party chair, Ian Lavery, has called them an “establishment tribute act” and the shadow foreign secretary, Emily Thornberry, told a rally on Saturday they had betrayed their party and that she would rather die than leave Labour.

Watson called on colleagues to “dial down the rhetoric”. “I was born into the Labour party, but I think dying is a virtue that’s overrated,” he said.

Asked whether he could join the defectors, he said: “I’ve been in the LP since I was 15 years old. You’d have to drive me out.”

•This article was amended on 24 February to remove a quote wrongly attributed to Jeremy Corbyn.