BRITAIN’S top-selling Sunday tabloid has vowed to take the “strongest possible action” if it is proven that its journalists hacked the phone of a missing teenager who was later found murdered.

British Prime Minister David Cameron said police should pursue their investigation into the claims about the News of the World, owned by Rupert Murdoch’s News International, in “the most vigorous way”.

News International is owned by same parent company as News Limited, publisher of The Australian.

News International chief Rebekah Brooks, who was editor of the paper at the time of schoolgirl Milly Dowler’s disappearance in 2002, told staff that the allegations were “sickening” and “almost too horrific to believe”.

“If the allegations are proved to be true then I can promise the strongest possible action will be taken,” said Brooks.

The tabloid has been dogged by claims of phone hacking ever since its royal editor and private investigator Glenn Mulcaire were jailed for the practice in 2007, and a new investigation was launched in January amid a wave of fresh allegations.

Mulcaire, who was paid by the newspaper, issued a statement to the Guardian on Tuesday.  “I want to apologise to anybody who was hurt or upset by what I have done,” he said, blaming the News of the World’s “constant demand for results”.

“A lot of information I obtained was simply tittle-tattle, of no great importance to anyone, but sometimes what I did was for what I thought was the greater good, to carry out investigative journalism,” he added.

Dowler disappeared aged 13 on her way home from school near London, sparking a high-profile search.

Her bones were found six months later, although it was not until last month that her killer Levi Bellfield was convicted.

According to the Guardian, private investigators and journalists listened to increasingly desperate messages on Dowler’s phone left by her parents and friends as the days went by without any word from her.

When her voicemail box became full, they even deleted several messages to make room for new ones — an action that her loved ones and police mistakenly took as proof that Dowler was still alive and using her phone, the report said.

“If they are true, this is a truly dreadful act and a truly dreadful situation. What I’ve read in the papers is quite, quite shocking,” Cameron told a press conference during a visit to Afghanistan.

He said police “should feel they should investigate this without any fear, without any favour, without any worry about where the evidence should lead them.

They should pursue this in the most vigorous way that they can”.

However, Cameron said he would not intervene in the government’s deliberations over News Corp’s highly controversial bid to buy the 61 per cent of BSkyB it does not already own.

“The government, on these processes, is acting in a quasi-judicial way and it is quite right that the Secretary of State for Culture, Media and Sport (Jeremy Hunt) carries out his role in that manner without any interference from anyone else in the government,” he said.

Police refused to comment on the allegations about Dowler, but Brooks said News International would cooperate fully with police, as well as conducting its own internal inquiries.

The Dowlers’ lawyer, Mark Lewis, said they would sue the tabloid for its “despicable” behaviour and called for Brooks to quit.

Police refused to comment on the allegations, but Brooks said News International would cooperate fully with police, as well as conducting its own internal inquiries.

Brooks maintained it was “inconceivable” that she had known about the actions and said she would remain in her position.  In the first sign of a commercial backlash from the allegations, carmaker Ford announced that it was pulling its advertising from the News of the World.

It has emerged that the parents of the victims in another prominent murder case, schoolgirls Holly Wells and Jessica Chapman, have been contacted by detectives investigating phone hacking at the newspaper.