Gideon Falter, chairman of Campaign Against Antisemitism, stated: "It is very sad that after nearly 40 years as a Labour MP, Frank Field felt morally compelled to resign the Labour whip because the party that was fiercely anti-racist when he joined it has now become infested with antisemitism".
Sky News's political correspondent Tom Rainer said Friday said that people close to Corbyn's office have pointed to Mr Field's conflict with his constituency party and the reason for his resignation was to avoid deselection - a mechanism being threatened against fellow Labour Brexiteer Vauxhall MP Kate Hoey.
Field called the Labour leadership "a force for anti-Semitism in British politics", according to a report published Thursday by the BBC, which quoted him as blaming a "culture of intolerance, nastiness and intimidation" in local parties.
In the letter, Mr Field said he would continue representing Birkenhead, where he was first elected as an MP in 1979.
"He said I would like you to withdraw your letter". It saddens me to say that we are a racist party.
Since unexpectedly becoming Labour leader in 2015 after decades spent on the left-wing fringes of the party, Corbyn has repeatedly faced accusations of turning a blind eye to antisemitic comments in the party and among groups he supports.
Under the Parliamentary Labour Party standing orders, which governs MPs, anyone who takes such action will usually get a letter asking them to retake the party whip within 14 days or face expulsion.
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"Following Jeremy's election as leader and the growth of party membership, which would in normal circumstances be welcome, we have become a party that displays intolerance, nastiness, and intimidation at all too many levels".
Mr Field also hit out at his local division of the party, describing it as the second factor that drove him to quit.
Mr Corbyn also stressed that people who hold anti-Semitic views "have no place in the Labour Party" and said people who use "anti-Semitic poison" are not his supporters, nor do they speak for him or the party.
He added that Labour must show it can put its house in order to demonstrate it is "fit to run the country".
Frank Field resigns from Labour party saying it is is now a "force for antisemitism".
He repeated that he would remain a member of Labour but added: "I can not, through continuing to take the Labour whip, lend any legitimacy to the most appalling culture which is now dominating national and local Labour Party institutions". "We can not afford to lose people of such weight and stature", he said.
They also said it would not be possible for Field to remain in the party having resigned the whip, despite his intentions to do so.
He plans to remain in parliament as an independent MP, and said he plans to stand at the next general election. In July, Labour members in Birkenhead constituency Labour party (CLP) passed a motion of no confidence in Field and called for the immediate withdrawal of the Labour whip.