Norris's application was thrown out by Lord Justice Leveson, Mr Justice Foskett and Mr Justice Hickinbottom.
Meanwhile, Lord Justice Leveson has summoned political blogger Paul Staines to appear before the inquiry.
Lord Justice Goldring ruled Thursday that the new inquest should start with the minimum of delay.
The group later said it believed the deal "can effectively deliver" Lord Justice Leveson's recommendations.
The Lord Justice General, Lord Hamilton, will deliver the judgment with Lord Kingarth and Lord Wheatley.
Lord Justice Leveson says the Press Complaints Commission has failed and must be replaced.
The action had resulted from comments about Lord Justice Girvan in Mr Hain's memoirs.
His paper has said it has "the gravest reservations" about Lord Justice Leveson's recommendations.
Lord Justice Leveson envisages a system that is independent of both the state and the press.
But on Monday, Lord Justice Pitchford, Mr Justice Foskett and Judge Peter Thornton QC dismissed the action.
BBC: Azelle Rodney lawyers 'can see' police surveillance film
After the report was published, the Independent praised Lord Justice Leveson for "rejecting statutory regulation as such".
Lord Justice Leveson said the journalists feared for their jobs if what they said was attributed to them.
In a ruling on 9 November, Lord Justice Leveson said he would be "prepared to receive anonymous evidence".
Lord Justice Leveson said he would recall Paul Dacre to face more questions on accusations by Hugh Grant.
Lord Justice Leveson insists that "this is not, and cannot be characterised, as statutory regulation of the press".
In the appeal court last week, Lord Justice Ward attempted to summarise the case from a religious viewpoint.
Up until now, Lord Justice Leveson has only held the future of the British press in his hands.
Lord Justice Leveson called for a new independent watchdog - which he said should be underpinned by legislation.
Lord Justice Underhill's judgement said that "the council never set out to consult about its outsourcing programme at all".
The question is being examined by an official inquiry led by a very senior judge, Lord Justice Leveson.
Lord Justice Clarke said he hoped both reports would be completed before Christmas.
His case has been rejected by the Lord Chief Justice, Lord Judge, Mr Justice Simon and Mr Justice Irwin.
Following his findings, Lord Justice Girvan was asked to terminate Mrs McDougall's appointment.
BBC: NEWS | UK | Northern Ireland | Victims' appointment not quashed
Judgements on the claims by Lord Justice Vos could create a framework for action from some 91 alleged victims.
Lord Justice Leveson had emphasised that he would not act as an arbiter.
David Cameron has backed the principles behind Lord Justice Leveson's recommendation for a tougher regulatory body for the press.
BBC: Leveson: David Cameron and Nick Clegg at odds over plans
Coroner Lord Justice Scott Baker was referring to allegations by Mohamed al Fayed.
The Sun and others have previously said they would accept everything recommended by Lord Justice Leveson - except statutory legislation.
Lord Justice GEOFFREY LAWRENCE (Nuremberg trial): Defendant Hermann Wilhelm Goering, the International Military Tribunal sentences you to death by hanging.
Lord Justice Leveson was speaking at a University of Technology Communications Law Centre symposium entitled Privacy in the 21st Century.
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