Mr Field, who will now sit as an independent Labour MP, told FTAdviser he intended to continue with his role on the committee, which he has led since July 2017.
Since the news of his resignation emerged statements of support for Mr Field to continue his work on the committee have come from various quarters of the pensions industry.
Mr Field, who was minister for welfare reform in Tony Blair's first government, has led the committee has it investigated the controversy surrounding the British Steel Pension Scheme and the role of advisers in this debacle.
He has also investigated the BHS and Carillion pension schemes as well as the effects of the pension freedom reforms.
Sir Steve Webb, director of policy at Royal London and former pensions minister, said "it is vitally important" Mr Field's decision to resign did not affect his current role.
He said: "Although we do not see eye to eye on every issue, there is no doubt that he is one of the most knowledgeable MPs in Parliament when it comes to pensions.
"In particular, I am sure that his pressure on the former owner of BHS played an important part in ensuring that BHS pensioners got a better outcome.
"I hope that MPs of all parties will support Frank Field in retaining this key role."
Baroness Ros Altmann, another former pensions minister, also supported the committee chair, saying: "I may not agree with Frank Field on Brexit, but on pensions and social benefits he is fantastic.
"No MP should face abuse or deflection for standing up for social justice and having a conscience."
The chairmanship of select committees is usually allocated by party, with most of these positions divided between MPs from the Labour Party or the Conservative Party before an individual is elected.
In a letter to Nick Brown, Labour's chief whip, Mr Field said it was resigning his party's whip over its handling of anti-Semitism allegations.
Mr Field said: "The current excuses for the party’s toleration of anti-Semitism must cease, and the party needs to regain its position as being the leading force against racism in this country."
"It saddens me to say that we are increasingly seen as a racist party," he added.
Mr Field added: "The party needs to send out a clear signal against nastiness, bullying, and intimidation at every level by taking effective action."
Mr Field will continue to serve as MP for Birkenhead and said he hoped to be in a position to seek the whip again as soon as possible.
In recent months the Labour Party has faced a large number of allegations of anti-Semitism, which have been capped by the release of a video of Jeremy Corbyn, the party's leader, claiming "Zionists" in Britain don't want to study history and "don’t understand English irony".
He has since said the word "Zionist" was being used "in the accurate political sense and not as a euphemism for Jewish people".
maria.espadinha@ft.com
