Media playback is unsupported on your device Media caption David Cameron told MPs if Andy Coulson lied he should be prosecuted

The judge leading the phone hacking inquiry will have powers to call media proprietors, editors and politicians to give evidence under oath, the PM said.

Lord Justice Leveson will oversee the public inquiry into the News of the World scandal and media regulation.

David Cameron said those who sanctioned wrongdoing should have no further role in running a media company in the UK.

The family of murdered Milly Dowler, whose phone was allegedly hacked, said they were "delighted" at the inquiry.

The prime minister held talks in Downing Street with Milly's parents, Bob and Sally Dowler, and sister Gemma - the third such meeting the family has had with senior politicians since revelations emerged that Milly's phone messages were allegedly accessed after she went missing in 2002.

Meanwhile, NoW's parent company, News Corporation, has dropped its bid to take full control of BSkyB.

Following fresh revelations about alleged malpractice at News International - News Corp's UK newspaper arm - Culture Secretary Jeremy Hunt had referred the company's bid to acquire the 61% of shares it does not already own in the broadcaster to the Competition Commission.

Despite the company's announcement, a Labour motion - backed by the Conservatives, the Lib Dems and smaller parties - calling on Rupert Murdoch's company to drop its bid was debated in the House of Commons.

Labour leader Ed Miliband said it was "unusual for a motion in this House to succeed before the debate on it begins" but News Corp's decision would not have happened without political pressure.

But Mr Miliband said it was a "painful truth" that politicians have been in thrall to the media for too long.

For the government, the Leader of the House Sir George Young said the Commons had "reflected the public mood" and was a "champion for its causes".

Former prime minister Gordon Brown spoke out against alleged law-breaking at News International on an "industrial scale" and said there were no private deals with the company when he was in Downing Street.

Turning to the inquiry, he said the rights of the public to information need to be balanced with the privacy of individuals.

In the US, senators have asked the authorities to investigate amid allegations that the phones of victims of the September 11 attacks may have been hacked into by News of the World journalists. News International has not commented on the claims.

The Homeland security committee chairman, Republican Peter King, called for an FBI inquiry. Democratic senators Jay Rockefeller and Barbara Boxer urged the attorney general and the Securities and Exchange Commission to investigate whether US laws had been broken.

Democratic senator Robert Menendez, who wrote to the attorney general separately, said the claims newspapers sought to "exploit information about... personal tragedies for profit" needed to be probed.

Meeting editors

Scope of hacking inquiry Culture, practices and ethics of the press

Their relationship with the police

Failure of current regulation

Contacts made and discussions between national newspapers and politicians

Why previous warnings about press misconduct were not heeded

Issue of cross-media ownership More detail on terms of reference News Corp drops BSkyB bid

In a statement, Lord Justice Leveson said his inquiry must "balance the desire for a robustly free press with the rights of the individual while, at the same time, ensuring that critical relationships between the press, Parliament, the government and the police are maintained".

He added: "The press provides an essential check on all aspects of public life. That is why any failure within the media affects all of us.

"At the heart of this inquiry, therefore, may be one simple question: who guards the guardians?"

Earlier, Mr Cameron told MPs the inquiry would begin as "quickly as possible" and would be in two parts - an investigation of wrongdoing in the press and the police and a review of regulation in the press.

He said Lord Justice Leveson, assisted by a panel of senior independent figures, would make recommendations for a better way of regulating the press which "supports their freedom, plurality and independence from government but which also demands the highest ethical and professional standards".

He will also make recommendations about the future conduct of relations between politicians and the press.

Mr Cameron told MPs he would require all ministers and civil servants to record meetings with senior editors and media executives to help make the UK government "one of the most open in the world".

Mr Miliband welcomed the proposals, arguing it must be imposed retrospectively, so that he and Mr Cameron publish all details of meetings with media executives dating back to the last general election.

Who is Lord Justice Leveson? Lord Justice (Sir Brian) Leveson became a barrister in 1970 and a QC 16 years later. The 62-year-old was made a High Court judge in 2000 and appointed to the Court of Appeal in 2006. He was senior presiding judge there from 2006 to 2009 and now, as chairman of the Sentencing Council, is responsible for criminal sentencing policy in England and Wales. Lord Justice Leveson is well known for being the barrister who led the prosecution case against serial killer Rose West, who was jailed in 1995 for the murder of 10 women and girls. He was also the judge during the 2006 trial over the murder of 10-year-old London schoolboy Damilola Taylor. In March, the Sun, a News International title, called him a "softie" for "introducing proposals to let 4,000 assault convicts a year go free rather than face jail".

Mr Cameron was previously criticised for meeting Mr Murdoch in Downing Street soon after the election, partly because Mr Murdoch did not walk through the front door.

Newspapers which did not support the government ran stories of "secret meetings".

Earlier, at prime minister's questions, Mr Cameron said a "firestorm" was engulfing parts of the media and police, and those who had committed offences must be prosecuted.

Mr Miliband said it was an insult to the family of Milly Dowler that Rebekah Brooks was still News International's chief executive.

Mr Cameron responded: "She was right to resign, that resignation should have been accepted. There needs to be root and branch change at this entire organisation."

Mr Cameron also told MPs that his former head of communications Andy Coulson should be prosecuted if it is proved that he lied when he claimed to know nothing about phone hacking at the News of the World while he was editor.

In other developments:

Press Complaints Commission head Baroness Buscombe welcomed the inquiry and said the organisation was "committed" to more effective regulation

News International's legal manager Tom Crone, who primarily worked at the News of the World and on the Sun, has left the company

The Sun has defended its story revealing Gordon Brown's youngest son Fraser had cystic fibrosis. It has released a video of the man it says was the source - the man's face is not revealed and his voice is disguised to protect his identity

The Australian arm of Mr Murdoch's media empire is to investigate all payments made to contributors since 2008

Ex-Labour MP Martin Salter says he intends to take legal action after allegations he was targeted by private investigators working for the News of the World.

Media playback is unsupported on your device Media caption Mark Lewis, solicitor: "The Dowlers are delighted that there will be a full, judge-led inquiry"

Meanwhile, Labour's communications chief Tom Baldwin is facing renewed questions over claims he handled private information which was gained illegally during his years at the Times newspaper, another News International publication.

The former Conservative deputy chairman Lord Ashcroft makes the allegations in a blog posting on ConservativeHome, which he owns. Mr Baldwin has not responded to the claims.

On Tuesday, former senior police officers told MPs the original inquiry into phone hacking did not get the attention it deserved because other duties would have been neglected, and News International failed to co-operate with them.

Sir Hugh Orde, president of the Association of Chief Police Officers (Acpo), said it was now time for News International to explain themselves - as the police had done, and hand over any evidence of corruption among police officers.