Tony Blair is to announce his “mission” to persuade Britons to “rise up” and change their minds on Brexit.
The former prime minister will say in a speech later that people voted in the referendum “without knowledge of the true terms of Brexit”.
He will say he wants to “build support for finding a way out from the present rush over the cliff’s edge”.
But former Cabinet minister Iain Duncan Smith said Mr Blair’s comments were arrogant and utterly undemocratic.
Downing Street has said it is “absolutely committed” to seeing Brexit through.
Prime Minister Theresa May wants to trigger formal Brexit talks by the end of March – a move which was backed in the House of Commons by MPs last week.
Mr Blair, who was UK prime minister between 1997 and 2007, will say in his speech to the pro-European campaign group Open Britain that those driving a withdrawal from the European Union “always wanted a hard Brexit”.
“Indeed even the term ‘Hard Brexit’ requires amendment. The policy is now ‘Brexit at any cost’,” he will say.
“Our challenge is to expose, relentlessly, the actual cost.
“To show how this decision was based on imperfect knowledge, which will now become informed knowledge.
“To calculate in ‘easy to understand’ ways how proceeding will cause real damage to the country and its citizens and to build support for finding a way out from the present rush over the cliff’s edge.”
Mr Blair, who campaigned to Remain in the EU, will say he accepts the verdict of June’s referendum, but would recommend looking again at Brexit when “we have a clear sense of where we’re going”.
He will also say the debate is being driven by immigration “which I fully accept is a substantial issue”.
“Nonetheless, we have moved in a few months from a debate about what sort of Brexit, involving a balanced consideration of all the different possibilities; to the primacy of one consideration – namely controlling immigration from the EU – without any real discussion as to why, and when Brexit doesn’t affect the immigration people most care about.”
Mr Blair has faced criticism in the past for his government’s decision to allow people from Poland, Hungary and the Czech Republic to work in Britain without restrictions, while most EU states imposed transitional controls to slow the rate of migration.
BBC political correspondent Tom Bateman said the former prime minister’s intervention on Friday is “quite an explicit rallying call” for those who campaigned on the Remain side, warning them that now is not the time to retreat but to “rise up in defence of what we believe”.
But he added that not everyone on the Remain side agrees with Mr Blair, with one former campaign boss arguing that they should be working for the best version of Brexit, rather than fighting against it.
A government spokesman said the British people had expressed their view very clearly on 23 June, adding: “There will be no second referendum.”
Iain Duncan Smith, who was a prominent Leave campaigner, said Mr Blair’s comments were arrogant, utterly undemocratic and showed that the political elite was completely out of touch with the British people.
Supporters of leaving the EU argue it will free up the UK to trade better globally and give the government better control of immigration.
Previously, Mr Blair has called for the views of the “16 million” people who had backed remaining in the EU not to be ignored.
He has argued that there has to be a way, either “through Parliament, or an election, or possibly through another referendum, in which people express their view”.
Earlier this month, MPs overwhelmingly agreed to let the government begin the UK’s departure from the EU by voting for the Brexit bill.
The draft legislation was approved by 494 votes to 122, and will move to the House of Lords on Monday.
But the Commons vote prompted splits in the Labour party, with shadow business secretary Clive Lewis quitting the front bench to vote against the bill. Despite calls by leader Jeremy Corbyn for his party to back the government, 52 MPs rebelled.
Lib Dem attempts to amend the bill to include a provision for another referendum were defeated by 340 votes to 33.
The government has promised to invoke Article 50 – setting formal talks with the EU in motion – by the end of next month, but it requires Parliament’s permission before doing so.