The last time I met Tony Blair in person, I got quite a shock. It was two years after he had left Downing Street, and the former prime minister resembled nothing so much as Francis Maude done up as a drag queen. Plucked and buffed, caked in makeup, his whole face gurned and twitched, the eyebrows and teeth performing a bizarre kind of eightsome reel. The man’s discomfort in his own skin was disturbing to witness.

The figure who greets me this week in the London office of his new Institute for Global Change is unrecognisably altered. The facial dance has vanished and he is strikingly composed; performative agitation has been replaced with centred gravitas. The cadence of his speech has changed, too; the curiously verb-less sentences are gone, along with the faux glottal stops. But then, lately, an awful lot about Blair’s life has changed, too.

In autumn last year, he announced the closure of Tony Blair Associates, his private business empire, and the winding up of complex and controversial financial structures that have earned him so many millions and so much opprobrium. Reserves of £10m, and henceforth 80% of his time, would be devoted to his not-for-profit work. Aged 64, he is returning to frontline British politics using his institute as a platform to promote progressive centrist policy ideas and combat the rise of populism. He categorically denies any plans to create a new political party, but confirmed last weekend that he has fully committed himself to a mission to reverse Brexit.

“To leave the European Union is just an extraordinary thing to do,” he says quietly. “It’s a decision to relegate ourselves as a country. It’s like being a top-six Premier League football club, and deciding to play in the Championship from now on.” Can he recall any historical precedent for a nation volunteering to demote itself? “Not in the modern developed world, no. And if you think it’s the most important decision this country has taken in living memory, then even if you think there’s only a small chance of it being changed, if you think that’s the right thing to do, you should be up arguing for it.”

Blair is perfectly aware that many, not least on his own side of the argument, consider him so toxic that any intervention on his part can only be counter productive. I’m curious to know if he factored this in before deciding to, as he has put it, “stick my head out the door” and “get a bucket of wotsit poured all over me”.

“Of course, there will be some people who refuse, literally refuse, to listen to you because it’s you. But my experience with people most of the time is that, if you’re making a reasonable argument, they’ll listen to you on that argument, even if they disagree on other things. In any event, frankly, if there was a stampede of people getting out there then I’d be very happy to be at the back. But I don’t notice this stampede. I think this is such a serious moment for the country that it’s your obligation to go out and state the argument.”

Blair believes it is still possible to prevent us leaving the EU, through a combination of grassroots pressure and parliamentary opposition. His problem, of course, is that, notwithstanding this government defeat on the EU withdrawal bill, his own party refuses to oppose Brexit.

“I understand it’s a very pragmatic position that the Labour party’s taking. And I don’t disapprove of pragmatism in politics at all. But I still think it’s the wrong choice. I think what the Labour party is essentially doing is saying: ‘There are a number of Labour voters who voted leave, and if we are painted as the anti-Brexit party, we’re going to lose that support. Therefore, what we should do is say: We’re going to do Brexit, and try to take Brexit out of the equation for our electorate, so they can vote [for us] on other issues.’ I completely get that. It’s a piece of political strategy. It’s actually what a lot of people would advise you to do.”

Still the legendary political operator of our time, Blair refers to “strategy” with the kind of objective respect a racehorse breeder might accord to a rival’s thoroughbred.

“I totally get it. But I think there are two problems with it. The first is that our language may be different, but we’re actually in the same position as the Tories, which is to say we’ll get out of the single market but we want a close trading relationship with Europe. Your risk is that, at a certain point, you get exposed as having the same technical problem that the Tories have, which is: here’s the Canada option, here’s the Norway option, and every time you move towards Norway you’ll be accepting the rules of the EU, but you’ve lost your say in it, and every time you move towards the Canada option you’re going to be doing economic damage. That’s the essential dilemma of the Tories, which I think will be exposed over time, and Labour’s got that problem, too.”

Blair’s second problem with the strategy is that it prevents Labour from making what he calls “an election-winning argument”. Voters, he argues, need to be told that all their concerns about jobs, public services, opportunities for young people and, crucially, the NHS, are correct and legitimate. “But Brexit is not the answer. You can make a huge point of not just the destructive impact of Brexit, but the distractive impact of Brexit, because it’s that distraction that means that this government has no time to deal with the health service. It’s got no time to deal with the problems of poverty. It’s got no time to deal with the problems of inequality. It’s got time to deal with one thing only. The whole country has been pulled into this Tory psychodrama over Europe.”

I wonder if Blair might, like many passionate remainers, be underestimating the public ferocity towards politicians who tell them they voted the wrong way in the referendum.

“Now of course, you’d have a huge fight. But you’d be fighting from a point of principle. Think of what a galvanising movement you would have in those circumstances, because you would actually be – well, for a start you’d be saying what’s right. That’s quite an important thing to start with. Secondly, I think the impact on the Tories would be really profound, because you’d be driving a wedge right into that Tory division – and the Tories are a profoundly divided party.”

Lots of Labour politicians I talk to share this view in theory, but argue that it’s hopeless in practice while the polls fail to indicate any significant shift in public opinion against Brexit. “And I say to them, ‘But what about leadership?’” Many believe the reason the country voted to leave was precisely to defy its political leaders; if they want the public to change its mind, invoking “leadership” is the last way to go about it. Blair rolls his eyes. “Guys, come on! I mean, what the hell are you in politics for? Of course, you’ve got to listen to people, but you’ve also got to lead them. You’ve got to be a bit more robust.”

Instead of telling leave voters they were wrong, I suggest, Labour could now have an opportunity to capitalise on Jeremy Corbyn’s own well-documented ambivalence towards Europe. Were Corbyn to say to the country: “I shared many of your misgivings. But having seen the harsh reality of what Brexit really looks like, I’m now convinced we shouldn’t do it,” would that convey both humility as well as leadership? Blair looks surprised, and pauses to consider this. “Yes. I think that’s a really good idea. I think that would be actually quite powerful. I agree, if Jeremy Corbyn was to say, ‘Look, I’ve always been sceptical about Europe, but I’ve now looked at this …’ Yes, that would be powerful.” He pauses again. “But you’ve got to want to do it.”

What does he mean? “You’ve got to want people to change their minds. I may be wrong about this, but I think there are elements of the Labour leadership who think that doing Brexit increases their possibility of winning power.” Does he mean they have calculated that it’s a strategic price worth paying for office? “Yes.”

Blair is certain this is a miscalculation. “I actually believe stopping Brexit is the route to win power.” But suppose they were right, I say, and supporting Brexit is indeed a strategic necessity for reaching No 10 – arguably not unlike new Labour’s 1997 electoral pledge to abide by Tory spending levels. Would Blair agree it’s a sacrifice worth making to win? “I don’t, actually. No. I think this principle’s too important. I do.” So given a straight choice between stopping Brexit and getting Labour elected, he would choose the former? “I’d like to see a Labour government in power. But I think the key national priority right now is stopping Brexit. I would put it above everything else right now for the country.”

The irony of Blair cast as the selfless politician willing to sacrifice power for principle, and Corbyn the power-hungry arch-triangulator, is not lost on either of us. “Yes, there is an irony in it, yes,” he agrees, smiling. “I’ve thought about that, too, and whether it’s me that’s forgetting what it’s like to try and win power.”

Labour’s performance at the polls in June caught Blair, along with most New Labourites, by surprise, so I ask what he had failed to see in Corbyn. He smiles again. “I think what he does have is a genuine personal charm. I’ll give him that. You know, when the rightwing media were trying to build him into some sort of demented Marxist, I think his demeanour was of enormous assistance. I pay tribute to that, I genuinely do. I mean, I actually admire that.” But he puts Labour’s success chiefly down to a Tory campaign “more incompetent than any I’ve ever seen ... And I don’t think the same rules will necessarily apply in the next election.”

Blair’s faith in the politics of the centre ground remains as ideologically implacable as Corbyn’s faith in socialism. But when the demographic centre of property-owning, middle-income middle classes is collapsing, is the political centre even relevant?

“We’re in an era when people want change. I still believe you can mobilise people to vote for a vision of the future rather than two competing visions of the past, one that is this nostalgic nationalism, which is what the Brexit thing amounts to in the end, and the other, these old-style, leftist policies of the 60s. If this is the choice, OK, then people are going to choose between those things. But I still think we’ve got a huge number of people who don’t really want either of those.”

Whether Blair can still connect with the centre is unclear to me. His repeated protestations in recent years that he is “never going to be part of the super-rich” are weirdly tin-eared from a man who counts his wealth in multiples of tens of millions. He is also conspicuously uncritical of Donald Trump’s presidency. Trump represents precisely the kind of populism Blair’s institute is dedicated to fighting – and yet, he says, were he still in office, he would have invited Trump to Britain, and would not have withdrawn the invitation following the infamous Britain First retweets. He told Alastair Campbell, in a GQ interview this year: “The left media finds it very hard to be objective on Trump,” and complained that Democrats “just go mental” when he even tries to suggest Trump’s administration could do anything good. Why does Blair find it all but impossible to criticise a US president? “Look, this will not appeal to much of your readership, but I really think it’s really important that America is strong in the world – clear, consistent and predictable with its allies. I always want to protect the relationship, because its important.”

But if nothing matters more to Blair than Brexit, presumably it’s even more important than our relationship with the US. What I don’t understand, I say, is why he doesn’t desist from making comments about Corbyn and Trump that will only alienate the very people in Britain he is trying to win over. Telling them they’re wrong about Corbyn, and wrong about Trump, feels like more of his old compulsion to chastise the left.

“I’m not telling people they’re wrong about Trump. I’m just saying it’s not a debate I want to get into at this point in time. And there’s no point in me saying: ‘I’ve now decided Jeremy Corbyn’s leadership is fantastic and I think he’s the answer to Britain’s problems’ – because you wouldn’t believe me.”

I can’t decide which surprises me more – Blair’s resolve to privilege speaking his mind over strategising, or the impression he conveys of a man restored to peace with himself. The two are almost certainly not unrelated. But I think I detect something else in his air of calm authority. Iraq had always seemed to be almost entirely about him – first as a vehicle for his ego, then as a battleground of his reputation. What makes his campaign against Brexit feel very different, and compelling, is a sense that it has little to do with him, and everything to do with the issue itself.

But is it winnable?

“I can’t predict it. I’ve given up predicting politics. I used to be really good at it, and then I was not so good at it, and now I think it’s probably inherently unpredictable. So where do you camp in those circumstances? You camp on the ground you believe in.”