Top officers forced to quit over the scandal also made frank admissions about Scotland Yard's close association with News International as they appeared before MPs.
Sir Paul Stephenson revealed almost a quarter of the force's communications team previously worked for the newspaper group.
John Yates - who quit yesterday as assistant commissioner of the Met Police - said it was time for News International to face up to responsibilities as he "confidently" predicted officers would be jailed.
Mr Yates said that last September he emailed Downing Street chief of staff Ed Llewellyn offering to brief David Cameron on aspects of the hacking inquiry.
"There was an offer in the early part of September 2010 for me to put into context some of the nuances around police language in terms of what a scoping exercise is, what an assessment is..." he said.
"That offer was properly and understandably rejected."
The PM's spokesman confirmed Mr Llewellyn was contacted by Mr Yates in September offering the PM an update on the inquiry.
But the official added: "Ed's response was entirely appropriate that he shouldn't be discussing operational matters with the PM."
Contact between Mr Yates and Downing Street emerged as the committee interviewed Sir Paul.
Pressed over why he had not disclosed to the Government that hacking suspect Neil Wallis worked for the Met as a PR consultant, Sir Paul said he was acting on guidance from a Government official.
Scotland Yard later clarified that "there was never any discussion with No 10 about Neil Wallis".
Both police chiefs said they resigned with their integrity intact.
But Mr Yates added: "I confidently predict that as a result of the News International disclosures a very small number of police officers will go to prison as a result of corruption."
In his last official engagement as commissioner at the Metropolitan Police, Sir Paul faced claims that ex-employees at the newspaper group were like "fashion accessories" as he admitted 10 of 45 members of media relations staff at Scotland Yard had worked for the newspaper group.
Giving evidence to the Commons Home Affairs Committee, Sir Paul said: "I understand that there are 10 members of the DPA (directorate of public affairs) staff who have worked in News International in the past, in some cases journalists, in some cases undertaking work experience with the organisation."
Sir Paul spoke of his "personally painful" decision to resign.
In an emotionally-charged final statement to the committee, he said: "I'm going because I'm a leader. Leadership is not about popularity, it's not about the Press, it's not about spinning."
Sir Paul said there had been "huge events, regrettable events" and he spoke of his "sincere regret" that Mr Yates had also chosen to resign.
Mr Yates told the committee he had quit because the phone hacking scandal had become a "huge distraction for me in my current role".
He added: "I think occasionally leaders have got to stand up and be counted. I've said I'm accountable for what's taken place on my watch.
"I firmly believe, and I'll reiterate that, I've done nothing wrong and my integrity is intact and my conscience is clear."
Dressed in full uniform, Sir Paul revealed that Home Secretary Theresa May had been "shocked" when told of his resignation decision and London mayor Boris Johnson accepted the news "very reluctantly".
The commissioner said he realised he had to go when it emerged that Mr Wallis had links to health spa Champneys, where he had received free accommodation and board following an operation to remove a tumour.
"I think it was very unfortunate for me," he said. "I had no knowledge previously. I think that, together with everything else, I thought this is going to be a significant story, and if I am going to be a leader and do the right thing by my organisation, I'd better do something quickly."
Sir Paul admitted that he was consulted over the employment of Mr Wallis, adding: "Just let me say, with the benefit of what we know now, I'm quite happy to put on the record I regret that we went into that contract, quite clearly, because it's embarrassing."
Sir Paul denied "impugning" Mr Cameron in his resignation statement, when he suggested his employment of Mr Wallis as a media adviser was less controversial than former News of the World editor Andy Coulson's appointment as Downing street communications chief.
"I was taking no such swipe at the Prime Minister," Sir Paul said.
Sir Paul said he was made aware that Mr Wallis was a suspect only "several weeks ago".
He also said he was told that Rebekah Brooks would be arrested "about two or three days before".
The committee heard he had 18 lunches or dinners with the News of the World and seven or eight with Mr Wallis over a period of roughly five years.
Sir Paul had earlier declared no knowledge of new claims that hacking suspect Neville Thurlbeck worked as an informer for Scotland Yard while he was a reporter at the News of the World.
When Dr Julian Huppert MP question him about his knowledge of a police source working at News International, the outgoing commissioner said: "I certainly would not have been aware of it."
Mr Thurlbeck, who was arrested on suspicion of illegally accessing voicemail messages in April, has admitted working as an official police source under the code name "George", the Evening Standard reported today.
Mr Yates also distanced himself from claims that he secured a job for Mr Wallis' daughter at the Met, describing himself simply as a "post box".
