Attorney general Dominic Grieve, who is presenting the case against the newspapersCredit: Anthony Devlin/PA
The case, presented by the attorney general, Dominic Grieve QC (pictured), will seek to determine whether the newspapers' coverage of the arrest of suspect Chris Jefferies were in contempt of court.
Lord Justice Dobbs and Mrs Justice Moses granted an application from Grieve to bring a case against the newspapers in May.
Yeates disappeared near her home in Bristol on 17 December after a night out. Her body was found in Failand, Somerset, on Christmas Day.
On New Year's Eve, Grieve issued a warning to the media about the coverage of the Yeates investigation. He will claim in court today that articles published by the Sun and the Mirror in the subsequent two days posed a "substantial risk of serious prejudice" to a potential trial of Jefferies.
Grieve adds in his submission to the court that the articles "for impeding the course of justice".
An application to the court in May claimed that the impact of the newspapers' coverage "could hardly be greater in relation to all the articles in terms of their prominence, presentation, subject matter, the use of photographs, other visual techniques, emotive language, the extent of the coverage on the issue in question and their general message".
Both newspapers deny liability in the case.
If found guilty, they could face fines and even prison sentences for individual staff.
Lawyers acting on behalf of Jefferies have also launched libel and privacy proceedings against several newspapers over the coverage of his arrest, with the Sun, Daily Mirror and Sunday Mirror, Daily Mail, Daily Star, Daily Express, Scotsman, and Daily Record all named as defendants.
Vincent Tabak, a 33-year-old Dutch engineer who lived next door to Yeates, has pleaded guilty to her manslaughter but denied murder. He is due to go to on trial for her murder in October.
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