The phone-hacking crisis consuming Britain’s biggest-selling Sunday newspaper has deepened on Thursday after reports that relatives of dead soldiers may had been targeted.

According to The Telegraph, Glenn Mulcaire, the private investigator at the heart of the scandal, had the personal details of the families of British servicemen who died fighting in Iraq and Afghanistan.

The Rupert Murdoch-owned News International group said it would be “absolutely appalled” if claims that its newspaper intercepted messages meant for the relatives of dead soldiers were true.

Britain’s Ministry of Defence was seeking clarification from detectives, who earlier contacted the servicemen’s families to warn them they may have been hacking victims, reported The Telegraph.

Murdoch has condemned as “deplorable and unacceptable” claims that the tabloid hacked the phones of relatives of murdered children and victims of the London bombings.

In his first statement on the affair, the Australian tycoon said his company would “fully and proactively co-operate with the police”.

British Prime Minister David Cameron has backed calls for a public inquiry into the allegations, but said police should first complete their probe of the “absolutely disgusting” claims.

Ahead of an emergency debate in the House of Commons, Cameron said: “We do need to have an inquiry, possibly inquiries, into what has happened.

“Let us be clear – we are no longer talking here about politicians and celebrities, we are talking about murder victims, potentially terrorist victims having their phones hacked into.

“It is absolutely disgusting what has taken place.”

But Cameron rejected calls by opposition Labour leader Ed Miliband for an immediate public inquiry “because you must not jeopardise the police investigation”.

Cameron also refused to back Miliband’s call for the resignation of Rebekah Brooks, the chief executive of News International who was editor of the News of the World when the hacking allegedly took place in 2002.

And he insisted the row should not affect the government’s decision, due within days, on whether Murdoch’s News Corp. should be able to proceed with its controversial bid to take full control of satellite broadcaster BSkyB.

The News of the World has been dogged by claims of phone hacking since its royal editor and Mulcaire, who was being paid by the paper, were jailed for the practice in 2007, with fresh allegations sparking a new police investigation in January.

Most of the victims identified so far have been politicians and celebrities, but it has now emerged that relatives of those killed in the July 7, 2005 attacks on the London transport network were also targeted.

Graham Foulkes, whose son David died in the attacks, told the BBC it was “just horrendous” to think someone had been listening to his calls.

Police said the parents of Holly Wells and Jessica Chapman, two 10-year-old girls murdered in Soham, eastern England, in 2002, may also have been targeted.

The most shocking revelation was that journalists hacked the voicemail of murdered teenager Milly Dowler after her disappearance in 2002, and even deleted some messages, potentially disrupting the police investigation.

Simon Greenberg, News International’s director of corporate affairs, told BBC radio it was “very close” to establishing who hacked Dowler’s phone.

As major companies including Ford and Mitsubishi withdrew their advertising from the tabloid over the scandal, Murdoch stepped in to limit the damage and give Brooks his full support.

“Recent allegations of phone hacking and making payments to police with respect to the News of the World are deplorable and unacceptable,” he said.

“I have made clear that our company must fully and proactively co-operate with the police in all investigations and that is exactly what News International has been doing and will continue to do under Rebekah Brooks’ leadership.”

In an email to staff on Tuesday, Brooks said she was “sickened” by the new allegations and said it was “inconceivable” she had sanctioned the hacking.

Meanwhile Gary Lineker is close to walking out on his role as a columnist at the News of the World over concerns that the newspaper’s involvement in phone hacking could damage his reputation, the Independent newspaper reported.

The former England footballer and host of the BBC‘s Match of the Day has held urgent talks with the editor of the newspaper, Colin Myler.

Lineker is understood to want further reassurances that those responsible for the culture of hacking are no longer involved with the organisation.

He had been earmarked to head a promotional campaign for the newspaper but, with the hacking scandal escalating, he has declined to take part.

Lineker is one of the most highly paid presenters at the BBC, and is said to earn (pounds sterling)1.5m a year.