Former Ukip leader Nigel Farage quickly tweeted "Good news" after judges scuppered the application by the two claimants – one of which even voted Leave in the referendum.
The pair were trying to tie Britain to a 'soft Brexit' by keeping it in the EU single market.
They were being propped up by a number of migrants who say they are living in a “state of limbo” in the UK following June’s Leave victory.
The case was brought by Adrian Walland and Peter Wilding, who run the pro-single market group British Influence.
Peter Wilding and Adrian Yalland have launched a new Brexit legal challenge
Mr Yalland and Mr Wilding, who coined the phrase ‘Brexit’, argued Brexit does not need to mean Britain leaves the single market – just the European Union.
Mr Yalland, who voted to leave, said: “I have campaigned for parliamentary sovereignty and accountable government for 20 years and now I want parliament to exercise its sovereignty by deciding if the UK should withdraw from the single market treaty.
Adrian Yalland voted Leave but doesn't think Britain should leave the single market
“Parliament, not government, took us into the treaty and so parliament, not government, must decide if and when we leave.
“I voted to leave the EU but parliament did not intend the referendum to cover the issue of membership of the EEA. The government should stop seeking to stretch the mandate to leave the EU to cover things parliament did not intend the referendum to cover.
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Sat, July 2, 2016
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Remain supporters demonstrate during the March for Europe rally in Parliament Square, London
“The referendum was on membership of the EU, not the EEA, nor of [the European Court of Human Rights]. It was not an opinion poll on immigration. I want nothing less than Brexit. But anything more than Brexit is for parliament to permit. The government has a mandate, not a blank cheque. We are a parliamentary democracy, not an elected dictatorship.”
Adrian Yalland has brought a new Brexit challenge to the High Court
The Brexit challenge was launched at the High Court this morning
Mr Yalland added Brexit could lead to the break-up of the United Kingdom.
He said: “An independent Scotland may be unlikely to join the EU, but it is a credible candidate for EFTA membership – which would give it full membership of the single market.
“The UK is party to the EEA agreement only in its capacity as an EU member state. Once the UK leaves the EU, the EEA agreement will automatically cease to apply to the UK.”
But Lord Justice Lloyd Jones, sitting with Mr Justice Lewis at a hearing in London, expressed concerns during the application hearing that the challenge might be premature.
And James Eadie QC, appearing for the Government, submitted: "This application is premature and should be dismissed for that reason."
The judges said they would give their reasons for blocking the application at 2pm.
More to follow…