Labour peer Baroness Kennedy QC, former Court of Appeal judge Konrad Schiemann and David Edward, a former judge of the Court of Justice of the European Communities, are among those who have called for a people's vote on EU membership.
In a letter to Mrs May, they say parliament should not be bound by the 2016 vote any more than it should be by the 1975 referendum that took Britain into the EU, especially when there are question marks over its validity.
They wrote that voters are entitled to know what they are voting for, and said: “There was a key difference between 1975 and 2016. The earlier referendum was held after negotiations were complete, so voters knew what they were voting for.
“In 2016, the nature of the negotiation process and its outcome were unknown. Voters faced a choice between a known reality and an unknown alternative.
“In the campaign, untestable claims took the place of facts and reality.”
Human rights specialist Jonathan Cooper, a barrister at Doughty Street Chambers, said: “The current state of the Brexit negotiations is worrying people throughout the UK and the legal profession is no exception to that.
“We represent people from across industry and society and we see every day the way the prospect of a catastrophic Brexit deal is already causing real harm.
“This letter to the prime minister has been signed by over a thousand of my colleagues who are convinced that not only is a people's vote the right thing to do, it is the most democratic thing to do as well.”
A Department for Exiting the EU spokeswoman said: “The people of the United Kingdom have already had their say in one of the biggest democratic exercises this country has ever seen and the Prime Minister has made it clear that there is not going to be a second referendum.
“We remain confident we will agree a mutually advantageous deal with the EU.”
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies