A top London law firm is taking action over Parliament's role in the process of the UK withdrawing from the EU.
Mishcon de Reya said Article 50 - which would need to be triggered to kick start the formal Brexit process – must not be invoked without an Act of Parliament.
The firm is acting on behalf of an anonymous group of clients, thought to include business people and academics.
It says a prime minister would be acting unlawfully if he or she triggered Article 50 without a full debate and a vote in Parliament.
Legal experts claim the move could make it less likely for Britain to leave the EU after the country backed Brexit by 52%-48%.
The government has said Parliament "will clearly have a role" in "finding the best way forward".
Kasra Nouroozi, a Mishcon de Reya partner, said: "We must ensure that the Government follows the correct process to have legal certainty and protect the UK Constitution and the sovereignty of Parliament in these unprecedented circumstances.
"The result of the Referendum is not in doubt, but we need a process that follows UK law to enact it."
Mischon says it has been in correspondence with government officials to seek assurances over the process.
It says that constitutionally, legislation is required to override the law passed in 1972 enshrining the UK's membership of the EU. This would mean an Act of Parliament would need to be passed by MPs.
A clear majority of MPs in the House of Commons backed staying in the EU during the referendum campaign.
Mr Nouroozi added: "The outcome of the Referendum itself is not legally binding and for the current or future prime minister to invoke Article 50 without the approval of Parliament is unlawful.
"We must make sure this is done properly for the benefit of all UK citizens. Article 50 simply cannot be invoked without a full debate and vote in Parliament.
"Everyone in Britain needs the Government to apply the correct constitutional process and allow Parliament to fulfil its democratic duty which is to take into account the results of the Referendum along with other factors and make the ultimate decision."
A Cabinet Office spokesman told the BBC: "As the prime minister said in the Commons, we have now got to look at all the detailed arrangements, and Parliament will clearly have a role in making sure that we find the best way forward.
"It will be important to ensure in moving ahead that the interests of all parts of the United Kingdom are protected and advanced."
