The controversial former prime minister used a major speech in central London to launch his campaign to reverse the EU referendum result.
Mr Blair insisted he agrees "the will of the people should prevail" but claimed his "mission" is to persuade the British public to go back on their decision to leave the EU.
The ex-Labour premier told an audience at Bloomberg: "The road we are going down is not simply hard Brexit it's now Brexit at any cost."
"Our calling is to expose relentless what the cost is."
Mr Blair admitted he "did not know if we can succeed" but insisted politicians will "suffer a rancourous verdict" in history over Brexit.
Mr Blair, who chose not to place immediate restrictions on immigration from new EU member states during his years in Downing Street, suggested migrants coming from the bloc were not the prime factor in the Brexit decision.
He said: "It's highly unlikely they are taking the jobs of British workers."
Instead, Mr Blair claimed voters were most concerned about immigration from outside the EU.
Referencing Nigel Farage's controversial Brexit campaign poster of Syrian refugees travelling across Europe, he said: "This immigration impacted the Brexit decision".
Tony Blair told Brexit supporters they 'voted without knowledge'
Warning Brexit is a "decision that begets other decisions", Mr Blair insisted there is now a "possibility of the break-up of the UK" with the issue of Scottish independence "on the table".
He added: "This time in a context much more credible for the independence case".
In an thinly-veiled attack on current Labour leader Jeremy Corbyn, Mr Blair claimed Labour's weakness as an opposition meant the part is not the "facilitator of Brexit".
He called for pro-Remain supporters to "build a movement across party lines" and to "find ways of concerting strategy and tactics" in the fight against Brexit.
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Mr Blair said: "We need to straighten the hands of the MPs who are with us."
Having recently closed his business interests, Mr Blair declared his new institute would provide a "policy platform" for anti-Brexit campaigners.
Mr Blair claimed people would argue the "will of the people wouldn't falter" but the ex-prime minister insisted it could.
He said others would argue "leaving is inevitable" but countered: "It isn't."
Mr Blair told pro-EU supporters: "This is not the time for retreat… but time to rise up."
He claimed they should continue "without fear" and "act in the true interests of Britain".
More to follow…