Mr Watson also criticised one of Mr Corbyn’s closest allies, saying reforms that were supposed to tackle racism in the party implemented by new general secretary Jennie Formby had “very patently” been unsuccessful.
The shadow cabinet member went on to call on colleagues including Emily Thorberry to “dial down the rhetoric”, after the shadow foreign secretary said she would “rather die” than leave the Labour Party.
It comes after a tumultuous week in which nine MPs walked out of Mr Corbyn’s party in frustration over antisemitism, his handling of Brexit and his leadership more broadly – with eight forming the new Independent Group alongside three ex-Tory MPs.
Discussing the scourge of antisemitic abuse within the party, which was a key factor in the departure of Jewish MP Luciana Berger, Mr Watson said: “He has said that it’s not done in his name. The problem is the test for us, the test for him as a leader, is to eradicate antisemitism, and it’s not other Labour Party members that will be the judge of that, it’s the British Jewish community.
“And I think he understands now, that if he is ever to be prime minister he needs to rebuild that trust. And the way you do that ... is to review those cases and go to the NEC [national executive committee], where he is in control.
“They will back him if he says these people need to be thrown out. And that’s the only solution now, because time is against us.”
Ms Formby arrived in post having previously worked for Len McCluskey at Unite the union, Mr Corbyn’s biggest financial backer.
She said she would make dealing with allegations of antisemitism in the party a priority, and brought in new rules to ensure they were properly dealt with.
But Mr Watson said they were inadequate: “The situation is so grave now that [Jeremy Corbyn] understands he needs to make a personal intervention.
“You know, we appointed a new general secretary and made it her priority to deal with it, and very patently the Jennie Formby reforms have not been adequate, they have not succeeded, and therefore it requires another sort of push.”
In impassioned language on Saturday, Ms Thorberry told a rally that she and others “would rather die than join any other party”, going on to attack those leaving as abandoning Labour to “cuddle up to the Tories”.
Mr Watson said: “I was born into the Labour Party, but I think dying is a virtue that is overrated.
“And I think it’s incumbent on all of us to sort of dial down the rhetoric, to try and understand the reasons that people feel they’re leaving the main political parties, to try and bring the country back together, that is divided by Brexit.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies