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
Rosa Bramley spoke about the reality of life in parts of London. Her friend became the third teenager to be stabbed to death in seven days.
Met Constable Thomas Hooper is said to have taken the medium-sized two-tier tin of biscuits from a storage cupboard.
7-year-old George Lockley has Spinal Muscular Atrophy which means he uses a wheelchair and is slowly getting weaker.