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".
This is not the time for retreat… but time to rise up.
Responding to Mr Blair’s speech, Vote Leave campaigner and Tory MP Michael Gove said: "People want politicians to get on with the job of making a success of leaving the EU rather than fighting old political battles. Tony Blair had his say during the referendum – he should now respect the fact that the British people voted to leave.
"When he won the general election in 2005 he had 9.5 million votes and a 2.8 per cent margin of victory over the Conservatives but he believed then that this mandate was enough to take the EU into the Lisbon Treaty, enough to give an extra £7 billion to Brussels when he agreed to cut our rebate, enough to agree to open our borders to new EU countries with no controls, and enough to hand over power to Gordon Brown.
"Politicians like Tony Blair should respect the result and work with the Government to make a success of Brexit instead of trying to undermine British democracy."
Fellow Tory MP and Brexit supporter Dominic Raab, a member of the Exiting the EU Select Committee, said:“However they voted in the referendum, most people have accepted the result and now want the UK to get on with making a success of its new place outside the EU.
“Tony Blair, who allowed uncontrolled migration from the EU when Labour was in power, refuses to accept the decision people made last June.
“He wants to go on putting the question over and over again until he gets a different answer.
"It is the height of arrogance and nothing could be more likely to convince the EU to offer the UK the worst possible deal than his suggestion that the decision could be overturned.”
More to follow…