Rebekah Brooks received a payoff worth about £7m after resigning as chief executive of News International at the height of the Milly Dowler phone-hacking crisis in July 2011.

The exact figure has never been disclosed by the Murdoch company – whose parent News Corporation holds its annual meeting on Tuesday – but one source said they believed it was between £6m and £8m.

An intimate of Rupert Murdoch, Brooks started out as a secretary at the News of the World in 1989, becoming editor of the News of the World and the Sun in succession.

She retained Murdoch's confidence as the phone hacking crisis intensified. After the News Corp patriarch flew into London in July last year, he took Brooks out for dinner, declaring that she was his "top priority" when questioned in the street by journalists.

The payoff package, far in excess of the £1.7m that was speculated about after her departure, comprised cash payments for loss of service, pension enhancement, money for legal costs, a car and an office.

News International declined to comment on the sum involved, but company insiders stressed there were "clawback" arrangements, which mean Brooks would have to pay some of the money back in certain circumstances.

It is understood that payback would be enforceable if Brooks was to be found guilty of a criminal offence relating to her employment. She is currently facing charges relating to interception of communications and obstruction of justice.

News Corp has not had to make any disclosure in public accounts, because its British companies have not reported their results to Companies House yet. News International companies have a financial year that ends on 30 June, so any filing covering the period of the Brooks payoff would not be due until next year.

The revelations about the size of Brooks's payoff are likely to be raised at the company's annual shareholder meeting at News Corp's Fox studios lot in Los Angeles. Some investors, such as the British group Hermes, are expected to vote against Rupert Murdoch remaining as chairman in the wake of the phone-hacking scandal, but the media tycoon controls 40% of the votes so he is unlikely to lose. The Independent newspaper reported on Tuesday that private emails between David Cameron and Brooks were withheld from the Leveson inquiry into press standards.

A government lawyer advised the prime minister that the emails involved were not "relevant". They were said to reveal the close friendship between Cameron and Brooks and were described by sources as containing "embarrassing" exchanges.

A Downing Street spokesman said: "All the material the inquiry asked for was given to them."

It is understood that there was an agreement between No 10 and the Leveson inquiry that Cameron would provide all emails and texts relevant to the News International bid for broadcaster BSkyB, as Cameron set out in his witness statement to the inquiry. Government sources said this was accepted by the Leveson inquiry and some texts or emails handed to the inquiry by Cameron, deemed to be on the margin of this definition, were not published by Leveson.

No 10 is not challenging the newspaper's claim that Cameron had sought legal advice on the nature of the exchanges to be given to Leveson.