Mr Jefferies was the subject of media scrutiny after he was arrested Two tabloid newspapers are set to go on trial for their coverage of the arrest of a man in connection with the murder of Bristol student Joanna Yeates.
Christopher Jefferies was arrested last December and he was later released without charge.
Attorney General Dominic Grieve said the Sun and the Mirror published stories which overstepped the mark.
If Mr Jefferies had gone on to be charged, he said they would have made a fair trial impossible.
BBC home affairs correspondent Matt Prodger said the case has far-reaching implications for the future of the Contempt of Court Act, which restricts the publication of material that could seriously prejudice a trial.
Miss Yeates, a landscape architect, vanished after returning to her basement flat in Bristol’s Clifton area on 17 December.
Her body was found on a grass verge about three miles away on Longwood Lane in Failand on Christmas Day.
Another man has admitted manslaughter and is awaiting trial.
Miss Yeates’ landlord, Mr Jefferies, who was the subject of media scrutiny after he was arrested, is also suing six national newspapers in the civil courts.
Our correspondent said the law of contempt has become the subject of much debate in recent months.
He said both the competition of 24-hour news and a relatively unregulated internet pose a significant challenge to the system of fair trials, which relies on juries reaching a verdict based only on the evidence they hear in court.
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