The judge did, however, give permission for the Core Issues Trust to appeal to the Court of Appeal.
Although she did not think such an appeal would succeed, she said there were "compelling reasons" to allow it to go ahead.
She said the case "concerns interference with the right to freedom of expression which is a matter of such fundamental importance that it merits consideration by the appellant court."
More top news
Scotland Yard said the male youths will appear in custody at Westminster Magistrates' Court on Saturday.
The family of Oliver Dearlove urged people to "think again" before using their fists, as the man who killed him began a six-year jail term.
London Fire Brigade took Southwark Council to court on four charges in relation to safety breaches at Lakanal House in Camberwell.