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."
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Police have released more images of people wanted in connection with what they describe as 'disorder' at a McDonalds in central London.
Four teenage girls, one of them aged 15, have been arrested following what police are describing as "disorder" at a McDonalds branch.