The letter to the Sunday Times has been signed by the country’s top business heads, including the former boss of Sainsbury’s Justin King.
MP Douglas Carswell tweeted with regards to the letter, saying: “Continuity Remain. They despise the views of ordinary folk.”
Economic adviser at Arbuthnot Banking Group Ruth Lea tweeted: “Please remind them the people have already voted.”
The business leaders have formed a group called Business for a People’s Vote, which will launch on Thursday.
One Twitter user, Colin tweeted: “The elites typified by greedy scum like Blair are openly declaring war on the public and democracy, hang them for treason! Home of democracy.”
The letter says: “The business community was promised that, if the country voted to leave, there would continue to be frictionless trade with the EU and the certainty about future relations that we need to invest for the long term.
“Despite the Prime Minister’s best efforts, the proposals being discussed by the government and the European Commission fall far short of this.
“The uncertainty over the past two years has already led to a slump in investment.”
The letter claims the country is heading for a “blindfold or a destructive hard Brexit” and the “ultimate choice should be handed back to the people with a People’s Vote”.
Although the letter does not directly refer to another referendum, it says the “ultimate choice” should go back to the electorate.
Other business chiefs to sign the letter are co-founder of Lastminute.com Martha Lane Fox, director of Twitter, Lord Myers and co-founder of the Innocent Drinks company Richard Reed.
This comes as 1,400 top lawyers have signed a letter urging the Government to hold a second vote on the referendum.
MP Bob Seely said of that letter: “What a surprise: 1,400 members of the Great and Good trying to overturn 17 million voters.
“They clearly want the UK to be more like the EU, i.e. where elites get to override democracy. Role on March.”
Last month, more than 700,000 people protested in London to demand a second vote on Brexit.
Theresa May has made it clear asking the public to vote again would be a betrayal of the public’s trust.
The Labour Party is opposed to a second referendum, calling for a fresh election in the event of a rejection of Theresa May’s Brexit plan in Parliament, but the shadow Brexit secretary Keir Starmer has said the party had not ruled out supporting a fresh vote.
London and Brussels hope to finalise an EU deal this month.