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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The 20-year-old was stabbed after the party was gatecrashed after details were posted on social media.
Incident commander Andrew O'Loughlin said the fire was exceptional but it looked as though it had "possibly done its worst" when he arrived.
The ambulance arrived a minute after Weihong Yu gave birth in Camden.