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 Labour MP expects the death toll in the Grenfell fire to be well above 79 and blames the disaster on Tory attitudes to social housing.
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