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
Rebecca Casserly was on her way to buy a coffee in north London when her phone was suddenly snatch from her hand by a man riding a bike.
Lee Curley took more than 120 pictures and videos of his attacks on the girl, said to be under the age of 13.
Council workers uncovered the AK-74 concealed in the undergrowth.