Frank Field has decided he will not trigger a byelection following his decision to resign the Labour party whip, citing the issues of antisemitism and bullying.

The veteran chairman of the work and pensions select committee said he would continue to represent his constituents and had been approached by the law firm Mischcon de Reya as he prepared to fight any attempt by Labour to expel him from the party.

The developments came as senior Labour figures, including John McDonnell, the shadow chancellor, expressed hope that the row could be solved without further political damage, and the Labour leader, Jeremy Corbyn, expressed bafflement at Field’s decision to resign.

Field stood down from the parliamentary whip on Thursday night after claiming Labour risked becoming a “force for antisemitism” and had allowed a “culture of nastiness, bullying and intimidation” that was “simply disgraceful”. He also refused to rule out forcing a byelection.

In an interview on Monday, Field told the Guardian he would not trigger a byelection, following approaches by constituents asking him to remain in his post. “People have told me to get on with my job as I have done for 40 years or so,” he said.

However, Field is still preparing to fight any attempt to force him to leave the party and has spoken to lawyers in Birkenhead and London prepared to help him mount a challenge. Labour said on Friday that he would have to leave the party if he failed to take the whip.

Field claimed several peers are members of the party and have not been obliged to take the whip.

“I said in the Guardian that I wanted the best lawyers and they approached me. I don’t want people to feel as if I am just going to go in and roll over. So I will fight on,” he said.

The Birkenhead MP, who recently faced a vote of no confidence from his local party over his support for Brexit, said he had spoken briefly to McDonnell since his resignation.

The shadow chancellor has suggested he should discuss antisemitism and bullying claims with Labour’s general secretary, Jennie Formby.

Field said: “There are some very serious points here about what action are we going to take action to root out the antisemites and whether that will that satisfy the Jewish community, who before all of this blew up did not feel under threat, and how seriously the party is going to take the bullying of Labour councillors.”

Last month, Mischcon de Reya helped Margaret Hodge mount a successful challenge against an attempt by Labour to discipline her.

Speaking on a tour of northern England, Corbyn questioned why Field had resigned the whip.

“Frank has been a Labour MP for a very long time, even longer than I have. I’ve known him for a very long time. I’ve worked with him in the past on social security and other issues,” he said in Liverpool.

“I’m sorry he’s resigned and I thank him for all the work that he’s done as an MP and for the party, but I don’t see why he had to resign.”