Uncertainty over the UK's European Economic Area (EEA) membership means ministers may be prevented from taking the UK out of the single market.
They would argue that the UK would not exit the EEA automatically when it left the EU and Parliament would need to decide.
However, according to the government, Britain's EEA membership would end with the country's exit of EU.
The single market allows tariff-free movement of goods, services, money and people within the EU.
The EEA, set up in the 1990s, extended the benefits to some non-EU members like Norway, Iceland and Liechtenstein.
Non-EU members though outside the Common Agricultural Policy and customs union, got barrier-free trade with the single market in return for paying into some EU budgets and accepting the free movement of workers.
If the courts backed the legal challenge and gave parliament the final say over EEA membership, then MPs could vote to ensure that the UK stayed in the single market until a long-term trading relationship with the EU had been agreed.
The pro-single market think tank British Influence is writing to Brexit secretary David Davis to inform him that it would seek a formal judicial review of the government's position.
"There is a strong chance that the UK will be acting unlawfully by taking us out of the EEA with Brexit," said the group's Jonathan Lis.
According to Professor George Yarrow of the University of Oxford, "There is no provision in the EEA agreement for UK membership to lapse if the UK withdraws from the EU."
However, a number of Conservatives have slammed what they call a "legal wheeze" to "frustrate the will" of the British people. According to pro-Brexit MP Dominic Raab, the lawyers needed to be working to make Brexit a success.
He said, "The public have spoken. We should respect the result and get on with it, not try to find new hurdles that undermine the democratic process," www.theweek.co.uk reported.