But Mr Cameron admitted he had had a word with Chief Whip Sir George Young.
Mr Cameron admitted that the recent figures were "disappointing but not unexpected".
David Cameron admitted "we're not doing enough to teach the next generation of programmers", and said there would be action on that.
Asked about the satirical comedy Yes Minister, in which civil servants famously sought to thwart government plans, Mr Cameron admitted there were "elements of truth" in it but dismissed "some of the characterisations in the papers".
Mr Cameron earlier admitted he still needed to convince the only UUP MP, Lady Sylvia Hermon, of the benefits of closer ties between the two parties.
But Ms Harman said David Cameron had admitted that Mr Fox had made "serious mistakes" and told MPs there was clearly a need for an investigation - particularly into whether Mr Werritty had profited from his association with the defence secretary.
Mr Cameron had earlier admitted in a speech at Moscow State University that there remained "difficult issues that hamper mutual trust and co-operation" between the UK and Russia.
The deputy prime minister, who admitted he had not seen Mr Cameron's speech, said he expected the prime minister to link any renegotiation of Britain's relationship with Europe and a future referendum to a new treaty.
Prime Minister David Cameron set up the inquiry after the News of the World admitted intercepting voicemail messages of prominent people to find stories.
Prime Minister David Cameron set up the inquiry after the now defunct News of the World newspaper admitted intercepting voicemail messages of prominent people to find stories.
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