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
Newly crowned double Formula One world champion Lewis Hamilton had a phenomenal season. Here is a look at his career and season in numbers.
Four men have been jailed for their part in the murder of a legal administrator, who was stabbed outside a pub on Borough High Street.
An American man has been sentenced to life in prison after travelling to the UK in a bid to murder a woman he met through online gaming.