Theresa May joined calls for embattled police and crime commissioner Shaun Wright to quit after a shocking report into child abuse in Rotherham, where he was a councillor responsible for children's services for five years.

The home secretary said that Wright, a cabinet member for children and young people's services at Rotherham council from 2005 to 2010, had "real questions to answer" about his position hours after it emerged that his own party, Labour, had asked him to quit.

May said: "It's not my job as home secretary to hire and fire police and crime commissioners. The whole point of them is that they are elected by the people, so ultimately it is a choice for the electorate.

"But I believe his own party have called for him to resign. I believe he has real questions to answer and I think in the circumstances he should heed those calls."

A Labour source said on Wednesday night that Wright's membership of the party would be suspended if he hadn't resigned by Thursday morning.

Earlier it emerged that Rosie Winterton, the Labour chief whip, telephoned Wright on Wednesday morning to ask him to resign.

It is understood that Winterton made clear that cabinet members, whether at a local or national level, should be accountable for failings that take place in their areas of responsibility. Wright, who had insisted he would remain in post, has returned home to consult his family on his future.

A Labour spokesman said Wright should step down in light of the "devastating" report.

"The report into child abuse in Rotherham was devastating in its findings. Vulnerable children were repeatedly abused and then let down. In the light of this report, it is appropriate that South Yorkshire police and crime commissioner, Shaun Wright, should step down," said the party spokesman.

While in office Wright received a number of reports about widespread abuse but failed to act swiftly enough, according to Professor Alexis Jay's shocking report on the sexual exploitation of 1,400 children over 16 years in the South Yorkshire town.

The call came as 15 victims announced plans to sue Rotherham council and South Yorkshire police in a class action. Their solicitor claimed that in each case both police and council "missed clear opportunities" to prevent the sexual exploitation of dozens of girls in Rotherham by gangs of men between 1996 and 2012.

David Greenwood of Switalskis Solicitors said: "In each of the 15 cases I am handling, there have been failings by individual social workers, but more importantly, we have been able to identify that Rotherham council and South Yorkshire police have failed to act on information which could have led to the arrest of perpetrators."

The message to Wright from Labour high command came after journalists asked Ed Miliband's aides whether the party leader thought Wright's position was untenable.

The position was immediately supported by the shadow chancellor, Ed Balls, and David Blunkett, the former Labour home secretary, who has represented the Sheffield Brightside constituency in South Yorkshire since 1987.

Within half an hour, Sarah Champion, the Labour MP for Rotherham, also said Wright had to go. She refused to respond to the Guardian on Tuesday when asked whether his position was untenable, but suggested on Twitter that she had changed her mind after reading Jay's full report.

At 1pm on Wednesday Champion tweeted: "Now fully read report, Sean [sic] Wright needs to step down as PCC. He's championed child abuse prosecutions since, but this happened on his watch."

In response to another Twitter user who suggested Labour in Rotherham needed a "clear-out", she added that there "needs to be full disciplinary & criminal inquiries".

Education minister Nick Gibb said those responsible for policy decisions which contributed to the scandal should be held to account.

He told ITV News: "It is quite appalling that the more vulnerable the children, the more horrific their stories, the less they are believed by the statutory authorities.

"And those that took those policy decisions, I think, should be held to account."

Just a few hours earlier Wright had insisted that he would not resign, saying he was not directly responsible and the council should take collective responsibility.

Wright told the BBC: "The scale of the problem has come as a surprise to me." He said he was not aware of the "industrial scale" of the abuse.

In an interview with Sky News he apologised for what he called a systematic failure. Wright said Jay should have gone further and "named names" in terms of council officials, politicians and police officers who had failed to protect youngsters from abuse.

Police and crime commissioners can only be removed by members of a police and crime panel.

On Wednesday some of the 13 panel members in South Yorkshire began to speak out against Wright.

Ralph Sixsmith, a Labour councillor on Barnsley council, said: "I think his position will be untenable. He's [Shaun Wright] unreservedly apologised, is that enough? Personally I don't think it is."

He said that Wright's history would taint his dealings with the police officers he had been elected to monitor, arguing: "I think if you've got to work with senior police officers … their perception of him as police and crime commissioner would be tainted by the fact that he was lead member of Rotherham council for children and young people's services for five years when this was going on."

Sixmith added: "If he's not stood down I think we are going to have to mention and ask is it untenable as it stands ... we hold him to account on issues that happen within our areas."

One of Sixsmith's colleagues on the police and crime panel in South Yorkshire said he was asking for a legal opinion on what powers the panel had to remove Wright if he refused to step down.

Terry Sharman, a Labour councillor in Rotherham, said: "What I will be asking for, and I'm waiting for an answer from legal to report back, is what position are we in to do something anyway? It's up to Shaun, he's got to make his mind up."

On Tuesday, another panel member Caven Vines, a Ukip councillor in Rotherham, said: "I think he should resign immediately and at the next meeting of the panel I will be standing up to say exactly that – I should hope the rest of the panel will join me. You can't defend the indefensible."

Kashaf Walayat, an independent member of the panel, said: "Those people that were involved in the decision-making process and had key roles need to be held accountable so the public can have confidence."

Roger Davison, a Lib Dem member of the panel, said: "I have no animosity towards him, but in this particular case it makes it difficult for him to continue."

Jay's report – commissioned by the council – said failures of the political and police leadership in Rotherham between 1997 and 2009 were blatant as the seriousness of the problem was underplayed by senior council managers and was not seen as a priority by South Yorkshire police.

Rotherham council's leader, Roger Stone, resigned on Tuesday following its publication.

The report, which looked at a period between 1997 and 2013, detailed "utterly appalling" examples of "children who had been doused in petrol and threatened with being set alight, threatened with guns, made to witness brutally violent rapes and threatened they would be next if they told anyone".

Jay said that children as young as 11 were raped by multiple perpetrators, trafficked to other towns and cities in northern England, abducted, beaten and intimidated.

The spotlight first fell on Rotherham in 2010, when five men were given lengthy jail terms after they were found guilty of grooming teenage girls for sex.