Vince Cable also has application for core participant status to the next stage of the inquiry rejected. 

George Osborne and Michael Gove have been refused privileged access to key evidence on the future of press regulation after Lord Justice Leveson rejected their applications for core participant status to the next stage of his inquiry.

The chancellor and education secretary, as well as the business secretary Vince Cable, had their applications for core participant status turned down in a ruling published on the inquiry website on Monday.

Leveson said the ministers' general interest in the inquiry was not sufficient to grant them special access to key documents.

This ruling came as core participant status was given to several victims of press intrusion, including Gerry McCann, the father of Madeleine, Bob Dowler, the father of Milly Dowler, and the actor Hugh Grant.

Prime minister David Cameron, deputy prime minister Nick Clegg and culture secretary Jeremy Hunt have also been granted core participant status for the inquiry's fourth and final stage.

The next module of the inquiry is focused on the future of press regulation. Unlike previous modules, the inquiry will publish proposals submitted by witnesses before they give evidence. Core participants will still be given advance sight of evidence to the inquiry – including detailed proposals put forward by other parties – and make representations on them. This phase of the inquiry is due to begin in the second week of July.

Unlike regular witnesses, core participants are able to ask questions of other witnesses and propose redactions and corrections to sensitive written evidence submissions.

Cameron and seven other cabinet ministers were given the status for the previous module of the inquiry – into relations between politicians and the press – but Leveson said that alone did not mean their core participant status should be automatically extended.

"I see real advantage in whatever assistance can be provided by those with responsibility for policy in the areas that are the subject matter of module 4 not least because the inquiry can be forewarned of practical issues which the relevant ministries have considered and may or may not have yet resolved in promulgated policy," the judge said.

"That is not to say, however, that all the ministers who were entitled to participate in module 3 are in the same position."

He explained that Cameron, Clegg, Hunt, and the justice secretary Ken Clarke were all "highly material" and policy oversight that is relevant to press regulation.

Leveson added: "The secretary of state for business, innovation and skills, the education secretary and the chancellor of the exchequer were properly involved as core participants in module 3 for different factual reasons; what might be their general interest in the inquiry (even enhanced by their cabinet responsibility for agreeing policy) is, however, not sufficient, in the exercise of my judgment and discretion, to justify granting that status to them for this module. In their cases, the applications are refused."

Leveson said proposed reforms to press regulations made by witnesses will be placed in the public domain before they are heard at the inquiry, allowing interested parties the chance to comment on them in advance.

Other parties granted core participant status for module four of the inquiry are: the Press Standards Board of Finance (PressBof), the body chaired by Lord Black that funds the Press Complaints Commission; Lord Prescott; Max Mosley; the solicitor Mark Thomson; the Lib Dem and Hacked Off campaigner Dr Evan Harris; and the pressure group Media Standards Trust.