The family of murdered schoolgirl Milly Dowler met the Prime Minister today and said they were "delighted" that a full, judge-led inquiry will be held into the phone hacking scandal.
Speaking on behalf of her parents Bob and Sally and sister Gemma in Downing Street, the Dowlers' lawyer Mark Lewis said: "The Dowler family are very grateful to the Prime Minister for another excellent meeting.
"At the start of this week the Dowler family wanted to have their voices listened to on behalf of them and on behalf of Milly and on behalf of all the other victims of unlawful activity by the press.
"There will now be a full public inquiry for the public, not a political inquiry for the politicians.
"The Dowlers are delighted that the Prime Minister has announced a full, judge-led inquiry, and they're particularly pleased that politicians for all three parties have liaised and reacted so quickly in response to the outrage of the public in respect not only of Milly but all the victims of such unlawful practices by the press, and failures in the pursuit by the police and failures by the politicians."
The family had already met Labour leader Ed Miliband and Deputy Prime Minister Nick Clegg to discuss phone hacking.
It is alleged that Milly's voicemail was accessed on behalf of the News of the World while she was missing, and that messages were deleted to make room for more recordings. This gave the family false hope that she was still alive.
Today's meeting was arranged by the Hacked Off campaign, which is pushing for tough action on alleged phone hacking.
Responding to the news that News Corporation's bid for BSkyB has been dropped, Mr Lewis said: "This was never a political thing. This shows actually the power of the public to stand up to something, however big an organisation is, however big, however far-reaching, however worldwide, to stand up and say 'something isn't right'.
"And like most scandals, this wasn't about the scandal itself, the malign conduct, it was about the attempts to cover it up. And when people cover up things, they are not fit and proper to run something."
He said they could not have predicted what would happen when it first emerged that Milly's phone was allegedly hacked.
"When the Dowler family first found out about this, when I first met them, no one could have known.
"It's an earth-shattering week for everyone concerned, for the Dowler family to know that actually the politicians and the people and the public would be behind them so much to say 'look enough is enough, this is too much press intrusion, too much power for one organisation and people have to stop and listen'."
Earlier today the Dowlers watched fierce exchanges over phone hacking in the House of Commons, as they sat in the public gallery to see Prime Minister's Question Time.
During the session, Mr Miliband said it was an "insult" to the family that News International chief executive Rebekah Brooks had remained in her job despite the scandal.
She was editor of the News of the World when Milly went missing in 2002.
Mr Cameron announced today that Lord Justice Leveson will lead a phone hacking inquiry that will have the power to make witnesses give evidence under oath.
Mr Lewis was joined at Number 10 by Martin Moore and Brian Cathcart from the Media Standards Trust (MST), which is running the Hacked Off campaign.
Campaign supporters Evan Harris and former senior police officer Brian Paddick also attended.
Prof Cathcart said campaign members would do all they could to make sure all aspects of the probe into hacking are made public.
Hacked Off supporters sought reassurance from the Prime Minister that the investigation would get to the bottom of whether politicians were involved in any alleged "cover up" of what had happened.
Former senior Met police officer Mr Paddick said Mr Cameron had agreed that the probe would not be limited to News International, and would cover any police force accused of failing to investigate hacking.
Downing Street said that Mr Cameron's meeting with the Dowler family was "constructive".
Mr Cameron's official spokesman said: "The Prime Minister has been keen throughout to underline the fact that we should be focused on the victims.
"This was an opportunity for him to hear first-hand from that family what they have been through."