Writing in the Telegraph today Parkinson, who is Rebekah Brooks' legal representative, said: "While those under police investigation have been permitted to maintain their silence on issues central to that process others have been questioned with few restrictions. As a result, much prejudicial material has come into the public domain."
Parkinson made his remarks in the Telegraph after Deputy Assistant Commissioner Sue Akers of the Metropolitan Police commented that there was a "culture of illegal payments" at the Sun newspaper. Attorney general Dominic Grieve is now examining Akers' remarks.
In an interview with BBC Radio 4 this morning on the Today programme Hill said that future criminal investigations against journalists are not threatened by Akers' comments.
"What Stephen Parkinson’s talking about is if there's a tidal wave of adverse publicity, will that have been forgotten by the time any trial - and we don’t know whether there will be one - comes about?"
Hill mentioned that the courts would assess whether there is a "substantial risk of serious prejudice to the proceedings" created as the result of publishing any material."
That is a risk at the time of those proceedings," he said. "So in other words the court will assess it when and if the individual comes for trial."
Defending the Leveson inquiry’s hearings of evidence, Hill added: "Lord Justice Leveson has said, look, he needs to understand the factual matrix that he’s dealing with in order to assess the evidence that he heard before Christmas.
"But openness and frankness of course are the hallmarks of any court proceedings."
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