The Prime Minister said the nation was 'appalled' by the allegations about the DJ which he said 'seem to get worse by the day'.
He called on every organisation involved with the star to get to the bottom of the alleged abuse and work out how it was allowed to happen.
His comments come as the BBC revealed today that it knew about allegations of abuse on its premises.
The Corporation issued a statement this morning admitting parts of a blog, written by editor Peter Rippon explaining why he canned the Newsnight investigation into the scandal, were 'inaccurate'.
It confirmed Mr Rippon had 'stepped aside' while a review into how the BBC handled the story was carried out.
Mr Cameron added today: 'So every organisation that was involved with him - whether the NHS or whether the BBC - needs to get to the bottom of what happened.
'The developments today are concerning because the BBC has effectively changed its story about why it dropped the Newsnight programme about Jimmy Savile.
'These are serious questions, they need to be answered. They need to be answered by these independent reviews that the BBC has established and I am sure that they will be.'
The BBC Trust, the corporation's governing body, said it was 'deeply concerning that there have been inaccuracies in the BBC's own description of what happened in relation to the Newsnight investigation'.
When Savile died aged 84 in October last year, Newsnight spent six weeks investigating allegations that the Top Of The Pops presenter abused pupils from Duncroft school in Surrey at the height of his fame in the 1970s.
BBC journalists spoke to women who claimed they had been abused or had knowledge of abuse at the school, which shut in 1980.
Newsnight reporters who led the investigation said that Mr Rippon had initially been enthusiastic about the programme, praising as 'excellent' their discovery that in 2007 the police had investigated allegations of child sex by Savile, but suddenly went cold on the story.
Mr Rippon, who published the blog on October 2, had written that Newsnight had no evidence against the BBC.
But the BBC said today: 'The blog says that Newsnight had no evidence against the BBC.
'No allegation was made to the programme that BBC staff were aware of Mr Savile's alleged activities, but there were some allegations of abusive conduct on BBC premises.'
Mr Rippon also wrote in his blog that women interviewed for the investigation had reported their alleged abuse to police. However, the BBC said today that in some cases that wasn't true.
It said: 'The blog says that all the women spoken to by the programme had contacted the police independently already and that Newsnight had no new evidence against any other person that would have helped the police.
'It appears that in some cases women had not spoken to the police and that the police were not aware of all the allegations.'
In addition, Mr Rippon wrote that there was no evidence staff at the Duncroft approved school in Surrey could have known about allegations that Savile abused children.
The correction now states 'In fact some allegations were made (mostly in general terms) that some of the Duncroft staff knew or may have known about the abuse.'
It adds: 'The blog says that all the women spoken to by the programme had contacted the police independently already and that Newsnight had no new evidence against any other person that would have helped the police.
'It appears that in some cases women had not spoken to the police and that the police were not aware of all the allegations.'
Conservative MP Rob Wilson told BBC Radio 4's The World At One: 'I think it is right that Rippon has stood down, but his position is pretty untenable all the same, given what has been revealed by Panorama and the journalists at Newsnight.
'There were far too many errors and omissions in his blog - and this blog, at the time, was used by the chairman of the BBC Trust and other senior management to try to belittle questions that I was putting them about the Newsnight inquiry, which was allowing them to be very dismissive and complacent in responses to me.
'The mess the BBC finds itself in is entirely unnecessary and entirely of its own making. The BBC and BBC Trust's handling of this matter has been absolutely lamentable. Both have shown weak leadership and poor judgment.'
The Savile scandal engulfing the BBC has been described as the 'worst crisis in 50 years' after damning emails last night revealed the full extent of its alleged cover-up.
And a bombshell Panorama investigation to be screened tonight alleges that Mr Rippon was under huge pressure from his bosses to drop the investigation in late 2011, shortly after the star's death.
This was despite him being warned by journalists that doing so would cause 'substantial damage to the BBC's reputation' and lead to allegations of a 'cover-up'.
BBC director-general George Entwistle - at the time the head of BBC Vision - was also warned that he might have to change his Christmas TV schedule if the Newsnight investigation was broadcast, because it could undermine glowing tribute programmes to Savile that had already been planned for the festive period.
Veteran BBC journalist John Simpson tells Panorama: 'This is the worst crisis that I can remember in my nearly 50 years at the BBC.
'I don't think the BBC has handled it terribly well. It's better to just come out right at the start and say we're going to open everything up and then we're going to show everybody everything.
'All we have as an organisation is the trust of the people that watch us and listen to us and if we don't have that, if we start to lose that, that's very dangerous.'
John Whittingdale, chairman of the Commons Culture, Media and Sport Committee which will take evidence from Mr Entwistle tomorrow, told BBC Radio 4's Today programme: 'I think from the BBC's point of view I think it is actually more damaging the suggestion that this was covered up in the last few months.
'What happened 30 years ago was terribly serious, it must be investigated.
'But the damage at the BBC today has been done by the investigation and the suggestions that the Newsnight investigation was dropped and various individuals were made known about it and did nothing.'
He outlined the areas his committee wanted to investigate. He said: 'I think there are a number of questions, the three main areas are firstly about how it appears that Jimmy Savile was able to behave in this way over quite a long period of time, sometimes within the BBC's own premises and yet nobody appeared to notice or do anything about it.
'The second question when it began to become clear that he was an abuser why the commissioning of tributes went ahead around last Christmas and whether or not George Entwistle, who was the director of visions at the time, had any knowledge.
'And then perhaps the most immediate question is around the dropping of Newsnight and the very serious suggestion in tonight's Panorama that the account given by the editor is not entirely accurate.'
Mr Whittingdale also told Sky News: 'Whilst Panorama say there is no evidence the editor was leant on from outside, the explanations originally given look very thin today.'
However, today the Evening Standard said that Lord Patten of Barnes, chairman of the BBC Trust, was recently heard pronouncing to senior BBC staff at a drinks party: 'It's probably good for George to have his first crisis early.'
Panorama's extraordinary revelations will be broadcast tonight, less than 24 hours before Mr Entwistle faces a grilling by MPs over the scandal.
MPs are also considering calling his predecessor, Mark Thompson, to give evidence.
In the programme Newsnight reporter Liz MacKean said Mr Rippon went cold on the Savile story, a switch she was convinced was because of pressure from above him at the BBC.
A few days later the BBC's head of news, Helen Boaden, told Mr Entwistle - who was at that time head of BBC Vision - about the Newsnight investigation and warned that if it went ahead it might affect the Christmas TV schedules.
Newsnight producer Meirion Jones, who was leading the Savile investigation, told Mr Rippon that the BBC would be accused of a 'cover-up' if they dropped the story, leading to 'substantial damage' to the BBC's reputation.
But after the Crown Prosecution Service told Newsnight that the reason it did not prosecute Savile in 2007 was because of lack of evidence, Mr Rippon decided to pull the investigation, explaining he did not think the story was 'strong enough'.
The Newsnight journalists were furious because the story was never meant to be about the police investigation, but about Savile's abuse.
Miss MacKean said: 'The story we were investigating was very clear-cut. It was about Jimmy Savile being a paedophile and using his status as a charity fundraiser and television presenter to get access to places where there were vulnerable teenage girls he could abuse.'
She told Panorama that she has also been extremely unhappy about subsequent repeated 'misleading' statements by the BBC about their reasons for dropping the programme.
A Panorama statement said: 'Peter Rippon has always maintained the story was pulled for 'editorial reasons' and not because of a potentially embarrassing clash with planned BBC tributes to Savile over Christmas.
'Panorama has found no evidence to contradict that view.'
Savile was labelled 'one of the most prolific sex offenders of all time' last week after police revealed he may have abused up to 200 victims.
Detectives are preparing to arrest the star's suspected accomplices as part of the investigation, and plan to question surviving celebrities and former BBC staff linked to him.
Those who face questioning may include paedophile pop star Gary Glitter, real name Paul Gadd, who is accused of raping a girl of 13 in Savile's BBC dressing room.
Separate and less serious allegations concern comedian Freddie Starr. Starr, 69, yesterday again angrily denied claims he groped a 14-year-old girl after a Savile TV show.
The BBC has announced two inquiries, one into its culture and practices, and another probing why Newsnight dropped its film.
Mr Entwistle, Miss Boaden and Mr Rippon last night declined to comment on the Panorama programme.
Full text of Rippon's retracted statements:
There has been a lot written about why I took the decision not to run a story into allegations of sex abuse by the former BBC presenter Jimmy Savile. It has been suggested I was ordered to do it by my bosses as part of a BBC cover-up. It has also been suggested that we deliberately withheld information from the police. Both these allegations are totally untrue and despite consistent strong denials keep getting repeated. I felt it would be useful to share more about what really happened.
The BBC has the highest editorial standards and with any story an editor has to weigh many things before putting something to air. BBC editors have a lot of power and responsibility and I have never, in the many years I have done this job, ever been told by one of my superiors not to do a story against my will. I would not still be working here if they had.
Why did I pursue this story about Jimmy Savile and why did I drop it?
I decided we should pursue the story because of the nature of the allegations and because the key witness told us the police had investigated the claims but the case had been dropped on the grounds he was too old. This made the public interest case from a Newsnight point of view potentially strong. If we could establish some sort of institutional failure we would have a much stronger story.
Some of the factors on the other side were: Newsnight is not normally interested in celebrity expose. Savile was unable to defend himself. What was the public interest served by reporting it given he is dead? The nature of the allegations and the level of proof required. The fact the incidents were 40 years ago.
We had no evidence that anyone from the Duncroft home could or should have known about the allegations. We had no evidence against the BBC. In her original statement our key witness said she was 'perfectly certain the BBC had no idea whatsoever of the goings on'. However, I felt if we could prove the police or the CPS had let the women down in some way we should go ahead.
We did establish the police had investigated the allegations in 2007. However, as the police would be obliged to investigate I wanted to check how they would respond to the allegation that it was not pursued because Jimmy Savile was too old. The CPS told us:
'The CPS reviewing lawyer advised the police that no further action should be taken due to lack of evidence.' The additional guidance noted stated. 'As this is the case, it would not be correct to say that his age and frailty was the reason for no further action being taken.'
This statement specifically denied the allegation that the investigation was dropped because of his age. I felt it was significant the guidance was included and we had not established any institutional failure and I judged it weakened the story from a Newsnight perspective. I took the decision not to publish. There were some of my team who disagreed strongly with my judgement, and others who agreed equally strongly.
However, those who disagreed accepted my decision. There were no rows of any kind as has been reported.
Did we withhold evidence from the police? No. We are confident that all the women we spoke to had contacted the police independently already. We also had no new evidence against any other person that would have helped the police.
Did my bosses order me to do anything? No. I did discuss it with my bosses in News in the same way I do any contentious story we are working on. I was told in the strongest terms that I must be guided by editorial considerations only and that I must not let any wider considerations about the BBC affect my judgement.
The fact that the BBC has the capacity to do this may feel odd to other organisations but it is fundamental to the trust we share with our audience.
There are a few repeat sentences in this article, I found it difficut to follow.