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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A man has died and two others have been injured in a stabbing outside Parsons Green Tube station.
Dany Cotton says referring to 'firemen' reinforces the stereotype that only men want to work in the fire service.
His heart completely stopped and one of his teammates performed CPR until paramedics arrived.