He indicated there will also be a second public inquiry into the original police investigation which failed to spot this week's revelations, which have included allegations that the News of the World hacked:
The families of victims of the London 7/7 terror bombings
The families of the two girls murdered by Ian Huntley - Holly Wells and Jessica Chapman
Milly Dowler, a 13-year-old schoolgirl abducted and murdered by Levi Bellfied
Sara Payne, mother of eight-year-old Sarah who was murdered in 2000
And there were fresh claims today from the BBC alleging the newspaper paid serving police officers for information.
The paper is now being accused of potentially hampering some of the most notorious child murder inquiries in modern times and police may be forced to re-examine every investigation into child murder or abduction since 2001.
Pressed by the Labour leader, Ed Miliband, to conduct a full public inquiry, the prime minister said he was "appalled" by the revelations and agreed that it was important that inquiries were conducted that were "public, independent, and have public confidence".
But he said that Rupert Murdoch's News Corporation's takeover of satellite broadcaster BSkyB would be allowed to go ahead suggesting that a U-turn would be illegal.
Mr Cameron said: “We do need to have an inquiry, possibly inquiries, into what has happened.
“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, and I think everyone in this House and indeed this country will be revolted by what they have heard and what they have seen on their television screens.”
The crisis at the News of the World was deepening by the hour as revelation has followed revelation, each one seemingly ever more shocking.
Ford, Vauxhall and the Halifax Building Society have already reportedly pulled their advertising with the News of the World and other blue chip clients are expected to follow suit.
The revelations are expected to cripple next Sunday's sales of the paper as the British public expresses their revulsion by voting with their purses.
Police today confirmed they had warned families of people murdered in the 7/7 terror atrocities in London that they may have been the targets of phone hacking by the News of the World, even as they mourned the death of love ones.
The scandal – which until this week had been understood only to involve celebrities – has moved to the very top of the British political agenda.
Graham Foulkes, whose 22-year-old son David was killed in the attacks, was told by police his details were found in a file marked 'July 7' during the police investigation and that he may have been hacked.
He said: “My wife and I were kind of all over the place and we were chatting to friends on the phone, in a very personal and in a deeply emotional context and the thought that someone might have been listening to that just looking for a cheap headline is just horrendous.”
Clamour was growing today for chief executive of News International Rebekah Brooks to resign.
She has so far said she has no intention of doing so, and historically she has had the backing of boss Rupert Murdoch.
However, if the revelations keep coming she may not have any choice.
She has said she had no knowledge of the actions of the journalists and investigators involved, despite being editor of News of the World at the time.
But actor Hugh Grant, who for months has led the calls for the News of the World to be called to account after his own phone was hacked, said: “She is either the worst editor in history or a liar.”
Simon Greenberg, Director of Corporate Affairs at News International, said this morning that the company was in 'fully co-operative mode' with the police investigation.