Lawyers at Mishcon de Reya argue that the British government cannot trigger Article 50, the legal process for leaving the EU, without a parliamentary debate and vote authorising it to do so.
"The result of the referendum is not in doubt, but we need a process that follows UK law to enact it," said Kasra Nouroozi, a partner at Mishcon de Reya in a statement.
"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."
As a majority of British lawmakers support remaining in the 28-member bloc, the legal challenge has the potential to complicate the process.
Mishcon de Reya said a "group of clients" was behind the legal action, without naming them, though The Lawyer magazine reported the clients were "a group of businesses".
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Once Article 50 is triggered, Britain has two years to negotiate the terms of its exit.
The British government said that the details were still to be worked out.
"We have now got to look at all the detailed arrangements," a spokeswoman for the Cabinet Office said.
"Parliament will clearly have a role in making sure that we find the best way forward."
Mishcon de Reya said it had been in correspondence with government lawyers since June 27, four days after the referendum in which Britain opted to leave the EU in a vote that crashed financial markets and sent shock waves through the continent.
One of the lawyers working on the case is Tom Hickman, co-author of an article that argued the British prime minister alone cannot begin Article 50 of the Lisbon Treaty.
Without an act of parliament, "the declaration would be legally ineffective as a matter of domestic law and it would also fail to comply with the requirements of Article 50 itself" it argued.
