The group behind the challenge believes leaving the EU is a separate action to quitting the European Economic Area (EAA) single market
The British government could be facing a new legal challenge over the implications of the Brexit decision.
The latest potential challenge will question whether leaving the European Union means automatic withdrawal from the European Economic Area (EEA) single market.
The pro-EU think tank, British Influence is writing to Brexit Secretary David Davis to seek clarification on the Government's position on the UK's EEA status when it severs ties with Brussels.
The group believes leaving the EU is a separate action to quitting the EEA - which extends the single market's tariff-free trade in goods to countries like Norway, Iceland and Liechtenstein.
A spokesman for British Influence told the Press Association: "It is likely there will be a legal action because, in our view, the Government has taken a stance that leaving the EU means leaving the single market."
The group's chairman, Peter Wilding told Sky News the action could potentially speed up the Brexit process.
"With one shot, if it is proved that if Britain leaves the EU it does not leave the single market, then the issue dies," he said.
"Consequently, Britain can get on with negotiating its departure from the EU whilst still being in the single market and therefore all the trouble and commercial and political upset goes."
A government spokesman said the UK would automatically stop being a member of the EEA once it leaves the EU.
"As the UK is party to the EEA Agreement only in its capacity as an EU member state, once we leave the European Union we will automatically cease to be a member of the EEA," he said.
He said the future relationship between the UK and the EU will be subject to ongoing negotiations.
"It's not in the UK's interest to give a running commentary on our thinking that could undermine our negotiating position,” he said.
"The referendum result will be respected and we intend to invoke Article 50 no later than the end of March next year."