Jeremy Corbyn insisted that Labour was united in tackling anti-Semitism as a senior peer quit the party, claiming the leader was surrounded by allies who were “hostile to Jews”.
Lord Mitchell said Mr Corbyn will never become prime minister but his allies have got Labour “by the throat”.
Former frontbencher Lord Mitchell, who is Jewish, blamed Mr Corbyn for being “lukewarm” about tackling anti-Semitism.
But Mr Corbyn hit back, insisting there was “absolute unity” in Labour in opposing “any form of anti-Semitism, any form of racism”.
Lord Mitchell said the Momentum movement of Corbyn supporters had seized control of Labour and the party was now a “lost cause”.
The entrepreneur, who served as a business spokesman for the party in the Lords under Ed Miliband, launched a scathing attack on Mr Corbyn following his re-election as Labour leader.
“Jeremy has no leadership qualities whatsoever, his little group like him and they think he’s the Messiah, but he will never become the leader and prime minister of this country,” Lord Mitchell told BBC One’s Sunday Politics.
Lord Mitchell, who was a founding member of the Social Democratic Party during the Labour split in the early 1980s, became a Labour peer in 2000.
He said he would not join another party but would instead sit as a crossbencher in the Lords where he would not be called a “traitor” for expressing his views.
Explaining why he would not fight for his position within Labour, he said: “My view is that it’s a lost cause, I think the Momentum people, Corbyn’s pals, have got this party by the throat and they’re never gonna let it go, at least not in my lifetime.”
The peer said in August that he would quit the party if Mr Corbyn saw off the challenge to his position, largely because of the anti-Semitism issue.
Following the decisive victory by Mr Corbyn over Owen Smith, Lord Mitchell said he was making good on his promise.
“I’m Jewish and I’m very strongly Jewish and I make no bones about it, and there’s no doubt in my mind that Jeremy himself is very lukewarm on this subject, he’s never been as vociferous in condemning anti-Semitism as he should be, and when he does make a mention of it he combines it with other forms of racism, so he will never say specifically as far as anti-Semitism is concerned.
“But even more than that, he surrounds himself with a coterie of people who hold violent, violent anti-Israel views and allied with it they are very hostile to Jews so, in my view, they’re pretty bad guys.”
Mr Corbyn rejected his comments, asking: “Has Lord Mitchell ever spoken to anyone in Momentum?”
The Labour leader said it was not fair for Lord Mitchell to claim that it was “very difficult” to remain in the party if you are Jewish and support Israel.
Mr Corbyn told BBC One’s Andrew Marr Show: “It’s unfortunate he would say that, because it’s not a fair comment and I would hope that he would reflect on that because clearly there are diverse views within the party on issues in the Middle East, but there is absolute unity in the party of opposing any form of anti-Semitism, any form of racism in the party. That is very clear.”