The open letter, organised jointly by The Independent and the People’s Vote campaign, has received significant backing since being launched just over a week ago.
It followed the latest People’s Vote march, which saw a million people take to the streets of London to demand a fresh public poll.
The letter reads: “We do not want the powerful to force on the people a Brexit that will damage the economy in both the UK and the EU, threaten the peace process in Northern Ireland, as well as lead to years more uncertainty and chaos.
“Please do not turn your back on this last chance to stop us turning in on ourselves. Allow us to check whether we want to proceed with this Brexit. Let us decide in a people’s vote.”
The Independent has been campaigning for a Final Say referendum since 2018 and has secured backing from more than 1.3 million people.
It comes as Boris Johnson signalled he will push on with plans for a general election after his pledge to take Britain out of the EU by the end of the month was left in tatters.
The prime minister will introduce legislation for a poll on 9 December if his bid for an election three days later fails on Monday night, as is widely expected, a No 10 source said.
Mr Johnson’s election bid on Monday, to be made under the Fixed-Term Parliaments Act (FTPA), would require a two-thirds Commons majority – 434 MPs – to agree to an election on 12 December.
But the Liberal Democrats and SNP have put forward a tightly-drafted bill that would grant an election on 9 December.
Labour is likely to abstain on Monday’s motion, according to reports.
Lib Dem sources said they would need to see any bill brought forward by the government before deciding whether to support it.
Earlier on Monday, Brussels accepted the UK’s request for a “flextension” until 31 January – enabling Britain to leave the bloc sooner if the withdrawal agreement bill becomes law.
Mr Johnson has previously said he would prefer to be “dead in a ditch” than miss the 31 October deadline.