Mr Justice Ouseley said he was refusing permission for a full hearing of the claim because of the long delay in bringing it forward and because of “the want of merit”.
The decision came as a bitter blow to campaigners, British expats living in Europe, who had crowdfunded the case, which was heard last Friday.
Called UK in EU Challenge, the case argued that breaches of campaign spending limits – punished by the independent Electoral Commission – meant the 2016 referendum was not a “free and fair vote”.
The campaigners had also based the case on what they saw as Ms May’s refusal to act on the growing evidence of illegality in the months since the Commission’s findings.
Vote Leave carried on spending, despite busting its limit two days before the June 2016 vote – and was later found by the Electoral Commission to have broken the law.
The campaigners had hoped to introduce evidence that its adverts reached “tens of millions of people” in those last crucial days – arguing it was enough to change the outcome.
The judge is continuing to give his ruling.
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