It comes after the 76-year-old resigned the whip over a "series of attempts" by leader Jeremy Corbyn to deny previous statements he made were anti-Semitic.
"First, the current excuses for its blatantly racist toleration of anti-Semitism must cease and we need to regain our position as being the leading force against racism in this country", he wrote.
He described a failure to act on what he called the "thuggish conduct" of some members demonstrates a "wilful denial" adding that, at worst, "it serves to legitimise appalling levels of bullying and intimidation of lifelong Labour supporters".
Commenting on Mr Field's decision to resign the Labour Party whip Oxton Liberal Democrat councillor Stuart Kelly told the Globe: "Frank Field's reasons for leaving the Labour Party are self-evident".
Field, who sent a letter explaining his decision to Labour Chief Whip Nick Brown, said he was resigning the whip as there was now a "culture of intolerance, nastiness and intimidation", in the party.
"Second, the party must recognise the culture of nastiness, bullying and intimidation that it has allowed to grow unchecked and expel local members whose public conduct is simply disgraceful". 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.
Veteran MP Frank Field has said he is considering triggering a by-election in his Birkenhead constituency.
Labour has been battling accusations of antisemitism for months, and leader Jeremy Corbyn has previously apologized for what he has described as "pockets" of antisemitism in his party. I shall of course remain a Party member as I have been since 1960.
Manchester United bully Burnley to prove Mourinho can still bring grit Premier League
A number of Mr Field's Labour colleagues have praised him and expressed their own concerns about their party.
But Corbyn-supporting members of Labour have criticised Mr Field's decision.
And Labour's Shadow Justice Secretary Richard Burgon said Mr Field should face a by-election.
"The party has taken the issue of anti-Semitism very seriously; far more seriously than any other political party".
Labour has been dealing with a row about the extent of anti-Semitism within the party for more than two years.
In a Facebook post, the group said there was "mounting pressure from the pro-Israel lobby, including right-wing Labour MPs", for the Party to adopt the full IHRA definition, which they said "equates criticism of Israel with anti-Semitism".
Corbyn has conceded that his party has a "real problem" with anti-Semitism in a recent newspaper article.
Allegations of anti-Jewish prejudice within Labour have grown since Corbyn was elected leader in 2015.