The 64-year-old former Labour Prime Minister said Britons had the right to change their minds on leaving the bloc as “new facts” surrounding Brexit became apparent.
Mr Blair told respected French daily newspaper Le Figaro: “My country has the right to change its mind, I want to fight for it. As the cost and difficulty of leaving the European Union become clearer, new facts become public, it is likely that citizens’ feelings about Brexit will change.
“When negotiations are over, whatever the agreement reached by the government, we must demand to have our say on it.”
He claimed it was only now, as issues such as the Brexit divorce bill became apparent, that people realised the impact Brexit would have, and so had the right to alter their opinions.
Mr Blair told the centre-right newspaper: “It is clear there will be a bill for Brexit and that there will be less money for health.
“People are also starting to realise that going out of the single market and the customs union is going to be extremely painful. It’s going back to forty years of integration and liberalisation.
“By the way, the single market was a big idea … British. The irony is that the single market and enlargement, which fuelled the vote for Brexit, were the two main European objectives pursued for years by the Labour and Conservative governments.
“I still believe that it is still possible to stop Brexit, even if the probability is less than 50 per cent.
“It is because the Conservative Party has said it will go to the end of Brexit no matter what the price, that it has lost a majority in Parliament in the last election. The Conservatives did not get the mandate they asked for.
“The atmosphere is changing in the country.”
Mr Blair, who governed the UK between 1997 and 2007, also said he wanted the Labour Party, now headed by Jeremy Corbyn, to take a stronger line on opposing Brexit.
He told the paper: “I am trying to convince the Labour Party to take a strong position against Brexit. I have the impression that he is moving in this direction. Then, we will see if some Conservatives are ready to choose their country rather than their party.”
He reiterated his view that Parliament should have the final say on any final Brexit deal, claiming Britons had “done an exchange without having seen the house”.
And he was pessimistic over the question of moving on to trade talks with the issue of Northern Ireland and its border proving to be a stumbling block.
He said: “I believe the most complicated immediate issue is Northern Ireland. Former Prime Minister John Major and I warned on this point during the referendum campaign. I do not see a solution to this question.”