MGN has been refused permission to appeal contempt of court ruling for its coverage of the arrest of Chris JefferiesCredit: Dominic Lipinski/PA
The Supreme Court today refused the appeal "because this was a very clear case of contempt of court".
The Mirror and the Sun were both found guilty of contempt of court in July and fined £50,000 and £18,000 respectively.
The three presiding judges found the newspapers' coverage of the January arrest of Jefferies had created "substantial risks to the course of justice" after the case was presented by Dominic Grieve, the attorney general.
News Group Newspapers, owner of the Sun, withdrew its application to appeal.
Today's decision said: "Permission to appeal was refused because the application does not raise an arguable point of law of general public importance which ought to be considered by the Supreme Court at this time and because this was a very clear case of contempt of court."
Jefferies, who was Yeates' landlord at the time of her death in December 2010, was arrested on suspicion of murder in January, but later released without charge.
In July Jefferies accepted an undisclosed sum in the high court after successfully suing the Sun, Daily Mirror, Sunday Mirror, Daily Mail, Daily Star, Daily Express, Daily Record, and the Scotsman for libel.
Yeates' neighbour Vincent Tabak, a 33-year-old Dutch national, was later arrested and was found guilty of her murder in October.
The attorney general presented the case against the Mirror and the Sun after warning the media at the time that coverage was at risk of prejudicing a trial.
At the time of the ruling he said that the decision was a reminder that the Contempt of Court Act applies from the moment of arrest, and not from the moment a suspect is charged.
Trinity Mirror did not wish to comment on the refusal of the appeal.