But in a newspaper interview in August 1983 - two months into Brittan's term as Home Secretary under Margaret Thatcher - Dickens revealed he had also sent a copy to the then Director of Public Prosecutions (DPP), Sir Thomas Hetherington.
Today the Home Secretary Theresa May was to make a statement on the affair in the House of Commons.
She was expected to come under pressure to explain how two government agencies were able to "lose" the dossier.
She was likely to be asked to reveal whether a previous Home Office trawl of its records included files held by security services.
Lord Tebbit, the Conservative former Cabinet minister, said on Sunday that there could have been a cover-up over a powerful child abuse ring.
"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 it was more important to protect the system than to delve too far into it," he told the BBC's Andrew Marr Show.
Asked if he thought there had been a "political cover-up" in the 1980s, he replied: "I think there may well have been. But it was almost unconscious. It was the thing that people did at that time."
The existence of a third copy of the dossier is likely to intensify demands for a full inquiry into allegations of organised child sex abuse, which Cameron has previously dismissed.
In the interview, published in the Daily Express, Dickens said he had spent two years investigating high-profile paedophiles. "I've got eight names of big people, public figures. And I'm going to expose them in Parliament," he told the newspaper.
"I have not enjoyed this crusade. It's been horrible. One of the people among those eight has been a friend of mine."
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*Cover-up claim as child abuse files disappear
David Mellor, who served under Leon Brittan as a Home Office minister, said the feeling at the time was that Dickens' dossier did not contain the shocking revelations he suggested. "My only recollection of this from my time at the Home Office was the suggestion there wasn't much to it," he told Sky News.
"The real crunch point for me is if - and I don't believe this for a millisecond - Leon Brittan had not taken appropriate action, Geoffrey Dickens lived for another 11 years and there is no evidence he went back and followed it up."
An MP who has played a leading role in disclosing allegations of sex abuse in Westminster called for an amnesty for police officers who were blocked from investigating allegations in the past.
Simon Danczuk, a Labour backbencher, said an amnesty would help resolve whether paedophiles in the heart of government had been the subject of a high-level cover up.
At least one former detective has told Danczuk he had been forced to sign a gagging order about his role investigating alleged paedophiles in the Government, and was frightened of the legal consequences of speaking openly about what he knew.
Police trace MP's 'victim' to US
Scotland Yard has tracked down a child at the centre of an alleged 1980s Westminster paedophile ring who has implicated a senior political figure.
The man - now in his 40s - is a successful entrepreneur based in the US and has given a detailed account of how he was assaulted. However, the alleged victim - who was initially willing to co-operate - has so far refused to make a formal statement to British detectives.
Police have traced a copy of a statement he gave more than 30 years ago as a child when he was rescued from horrific sexual assault. His version of events is understood to be corroborated by a detective who conducted the official interview with the child at the time.
A US law enforcement officer was asked to interview the man on Scotland Yard's behalf this year. The alleged victim is understood to have named the senior figure. During his original interview in 1982 the child referred to his abuser working at "the big house", which detectives believe was the Houses of Parliament.
Detectives interviewed a retired officer who was involved in the original investigation and who interviewed the alleged victim. The Daily Telegraph understands the detective was reluctant to go into detail about why information about the politician was not included into witness statements at the time or submitted into evidence as part of a potential prosecution. His reluctance is understood to have stemmed from his fear that he could face disciplinary action, or other legal implications, or lose his pension.
- additional reporting Independent
