Former Liverpool Council deputy leader Derek Hatton has withdrawn his application to rejoin Labour.
The former Militant firebrand, who was expelled from the party in 1986 because of his membership of the group, had been readmitted to the party in February. He was then suspended by the Labour Party less than 48 hours later.
The suspension was over social media posts made in 2012.
Labour’s ruling National Executive Committee (NEC) had been due to review the 71-year-old’s application on Tuesday.
A party spokesman said: “Derek Hatton has withdrawn his membership application and is therefore not a member of the Labour Party.”
His decision to withdraw his application is understood to have come before the committee had considered his case.
Mr Hatton, was originally expelled by the then leader Neil Kinnock for membership of the left-wing Militant Tendency.
It followed a national outcry in the 1980s after the council set an illegal budget and then sent out redundancy notices to thousands of staff by taxi.
He and other members of the Trotskyite group known as the Militant Tendency were widely blamed for making Labour unelectable when Neil Kinnock was party leader.
The possible readmission of the outspoken left-winger drew criticism from some MPs earlier this year .
Shadow international trade secretary Barry Gardiner told the Commons he had written to the Labour Party’s general secretary and “lodged a formal complaint” against Mr Hatton.
Gardiner’s comments followed Labour MP Neil Coyle saying Mr Hatton had tweeted “what seemed to imply that every Jew, wherever they live in the world, is responsible for the actions of the Israeli government”, adding: “Does he share my view that Derek Hatton has no part to play in our Labour Party?”
The shadow cabinet member replied: “This morning I saw the reports about not just the readmission of Derek Hatton but the tweets he has mentioned.
“I wrote to the general secretary of our party, I lodged a formal complaint. I understand that action has since been taken in respect of the complaint and I’m sure that I will be looking out to see precisely what appropriate action is taken in due course.
“I totally agree with you. I think it was a travesty that, at least I think many of us knew for some while that he had applied to rejoin the party, but for the news of his readmission to come to public attention on the very day when some members of our party were forced out – I think it was appalling.”