Tony Blair has urged pro-Europeans to "rise up" and persuade the British people they were wrong about Brexit.
In a keynote speech, the former prime minister said voters had backed leaving the EU without knowing the true cost and should have the opportunity to change their minds.
Speaking at the headquarters of the Bloomberg financial news agency in London where David Cameron first set out his plan for an in/out vote on Britain's EU membership, he questioned whether the referendum had given a mandate for "Brexit at any cost".
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"I accept right now there is no widespread appetite to re-think. But the people voted without knowledge of the true terms of Brexit.
"As these terms become clear, it is their right to change their mind. Our mission is to persuade them to do so," he said.
"What was unfortunately only dim in our sight before the referendum is now in plain sight. The road we're going down is not simply hard Brexit. It is Brexit at any cost.
"Our challenge is to expose relentlessly what this cost is, to show how the 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 our country; and to build support for finding a way out from the present rush over the cliff's edge.
"I don't know if we can succeed. But I do know we will suffer a rancorous verdict from future generations if we do not try."
Mr Blair said that in the absence of an effective opposition, pro-Europeans needed to build a "movement " that reached across party lines.
He said that the institute which he was launching would play its part in developing the arguments to rethink the country's position.
"The debilitation of the Labour Party is the facilitator of Brexit. I hate to say that, but it is true.
"What this means is that we have to build a movement which stretches across party lines; and devise new ways of communication," he said.
"These groups must find ways of concerting strategy and tactics effectively. We should begin to create informal links immediately and then build them into a movement with weight and reach.
"We need to strengthen the hand of the MPs who are with us and let those against know they have serious opposition to Brexit at any cost."