Len McCluskey said Labour MPs threatening to quit the party if Rebecca Long-Bailey replaces Jeremy Corbyn as leader should go now.
The leader of the Unite Union, who was central to Corbyn's leadership of the party, said that it was "disgraceful" that MPs were threatening to resign.
On Radio 5 Live's Piennar's Politics show this morning, he said: "If you want to give me some names then we can debate that with them.
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"The truth of the matter is if any Labour MP hasn't learned the lesson we need a united party - remember Jeremy Corbyn for four years had to fight not just the enemy, the right wing newspapers, but indeed our own ranks - now if people haven't learned that the British electorate do not like a divided party and want to continue the divisions after this leadershiop election, frankly they're better to clear out now rather than mess us about."
When told the MPs would quit rather than stay in the party if Long-Bailey wins the leadership election, he added: "Good riddance."
Long-Bailey is seen as the "continuity Corbyn" candidate, and gave him ten out of ten for his leadership, despite the party failing to win at the last two general elections, while it was also caught up in an internal row over anti-Semitism.
Mr McCluskey's union has already officially backed Long-Bailey in the contest, and also thrown its weight behind Richard Burgon as the next deputy leader.
Today he dismissed suggestions that Unite, Labour’s biggest trade union backer, would have its influence reined in under a new leader, adding that those hoping for a change at the top were “deluding themselves”. As long as he led Unite, he said, he would "continue to be an influence".
And he said the Labour Party had been changed forever by Jeremy Corbyn’s leadership and that his legacy will be taken forward no matter who the new leader is, even if it’s the more centrist Sir Keir Starmer.
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He told John Pienaar that he believed Starmer, who is seen as a more moderate candidate for the top job, would carry forward Corbyn’s ‘radical direction’.
Mr McCluskey said : “In my view, I think this is Corbyn’s legacy, I think Labour has changed forever. We now have a Labour Party who offers an alternative and that's perfectly good for the democracy of our country. How many times did all of us hear people say politicians are all the same, there's no difference between them.
"What Corbyn has effectively done, he and John McDonnell, have created an alternative to the Conservative Party. “
He said of Keir Starmer, Rebecca Long Bailey and Lisa Nandy "all of them are running on a platform of believing that the radical direction of the Labour Party will not change.”
"Keir himself has said 'we are not going backwards' so I think that is the nature of the legacy of Jeremy Corbyn.”
Mr McCluskey also said he believed that Labour lost the election because of its stance on Brexit and that he had tried to warn Corbyn that the policy was jeopardising their chances of winning. “It was predominantly Brexit and some of us were,including myself, were pointing this out to the leadership for over 12 months.
“The more that Labour slid into being perceived as a Remain party the more we were saying that there would be consequences in our heartlands and unfortunately that came about,” Mr McCluskey said, although he added that in hindsight “there were too many policies” and that introducing a new policy “every single day” meant people couldn’t focus on the overall message.
Asked which policies he believes Labour should drop, he added: "That'll be up to the leader, whoever it is. It'll be up to them to make a judgement how to prioritise our policies."