He was speaking ahead of the expected announcement by his government of a wide-ranging inquiry into the alleged abuse and whether the authorities ignored it.
"I am absolutely determined that we are going to get to the bottom of these allegations and we're going to leave no stone unturned to find out the truth about what happened -- that is vital," the prime minister said.
Long-running rumours of an organised ring of paedophiles in Westminster have resurfaced following revelations of historic child abuse by celebrities such as the late BBC presenter Jimmy Savile.
It was passed to the Home Office, or interior ministry, but subsequently went missing.
Following a review last year, the ministry has now revealed that in total, 114 files relating to child abuse allegations it received between 1979 and 1999 were "presumed destroyed, missing or not found".
It has also identified 13 "items of information" about alleged child abuse, four of which had not been reported to the police, although detectives have now been informed.
"At that time I think most people would have thought that the establishment, the system, was to be protected and if a few things had gone wrong here and there that it was more important to protect the system than to delve too far into it," he told the BBC.
Home Secretary Theresa May, who currently heads the Home Office, is expected to announce a broad independent inquiry into how the government dealt with the allegations of abuse.
Meanwhile the minister who led the Home Office at the time the Dickens dossier went missing, Lord Leon Brittan, issued a statement today insisting he had behaved appropriately.
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