British Influence wrote to Brexit secretary David Davis to warn it would seek a judicial review, arguing that EEA membership could both keep the UK in the Single Market and support Theresa May's desire for migration reform.
However, the government has warned that it considers EEA and EU membership to be a single issue.
A Downing Street spokeswoman said : “The UK is only part of the EEA agreement in its capacity as an EU member state. And once we leave the European Union we will automatically cease to be a member of the EEA – that is the legal framework.”
And now the referendum's official Remain camp, now rebranded as Open Britain, has refused to back the plan, warning it would rather convince the government of its arguments than pursue court battles.
Open Britain co-executive director Joe Carberry, said: “More and more evidence shows how difficult and detrimental leaving the single market would be. We are focusing on making a positive argument for Britain’s place in the Single Market, which is vital for jobs and growth in our country. Anything else would erect trade barriers and hit British business.
“At the same time, we fully accept the verdict of the British people in the referendum. We fully believe we can win that argument in Parliament and in the country, whatever the courts happen to decide.”
British Influence argues that, similarly to Article 50 and the EU, departure from the EEA requires the government to trigger Article 127 of the EEA agreement.
QC Jolyon Maugham told the BBC: “That might well, and I think it probably would, require a separate a further act of parliament and that may mean more delay.”
A self-described “Remoaner”, Maugham added: “Personally I wouldn't vote against the triggering of either provision, but I do want to leave the door ajar to see what the evidence shows about the consequences of those articles being triggered upon the economic health of the nation, before we finally leave.”
It comes as Downing Street prepares to resume its legal battle with campaigners over the right to begin Brexit without parliamentary approval.
Government lawyers will take the fight to the Supreme Court next week having lost out in the High Courts in early November.