It is the most bitter-sweet of anniversaries. Twenty years ago on Monday, the country chose to put him into power with the largest parliamentary landslide ever secured by Labour. I was there to watch the victory celebrations on the south bank of the Thames as a fresh-faced, pre-grey and enormously popular Tony Blair waited for the sun to rise over the river before he declaimed “a new dawn has broken” to the exultant crowd. Reminded of happier times and his younger self, he remarks: “You’ve aged better than me.”

Blair has always deployed a charming line in self-deprecation, but today it is allied with a passionate desire to remind people of the many advances made possible only by his unique feat of winning three back-to-back terms for his party. “What I did in respect of Labour, I look back on with pride,” he says, and rattles off a long list of the “huge achievements” of his time in government: the minimum wage to civil partnerships; greatly increased investment in schools and hospitals to big reductions in child and pensioner poverty; the Good Friday agreement in Northern Ireland to the trebling of the budget for international aid. Many of his reforms were ferociously opposed by the right at the time and ultimately entrenched when the Conservatives felt compelled to accept that he had shifted the centre of political gravity.

He adds the not unreasonable observation: “There was a different atmosphere. We became a much more modern and progressive country.” This is not just the self-flattery of an ex-leader. At what looks like a bleak juncture for his brand of politics “it’s very important for progressive people to be proud of what they did together”.

This anniversary is also an anguished one because it coincides with an election that every indicator suggests could very well leave Labour buried under a landslide for the Conservatives. Even Sedgefield, his seat in parliament for 24 years and Labour forever, appears to be in peril of engulfment by the Tory tidal wave. How did the party that he led to an unprecedented hat-trick of victories reach such a dark place?

“We created a coalition that was a coalition of people who were modern-minded, but believed in social justice. The trouble is that if you don’t represent them, then an alternative view, which is a closed-minded view of the world that goes Brexit, anti-immigration, isolationist, that view can command the majority.” Though he is generally restrained with his criticisms now that election battle is engaged, his despair with Jeremy Corbyn’s Labour is barely disguised. “Where you’ve got a hard Brexit Tory party and a hard left Labour party, you will find a lot of homeless people. If from the progressive side of politics you offer people a vision that looks like the past, then I’m afraid you’ll lose that group of people in the middle who would be prepared to go for you provided they felt you understood the modern world.”

Twenty years on from 1997, and nearly a decade since he departed No 10, there is not a settled verdict on Blair’s record. His premiership is still ferociously litigated and not just because of Iraq. He is vilified by the right, many of whom cannot forgive him for beating them three times in a row. “Why do you think the Daily Mail attack me every week, sometimes every day? It’s because they know that if my brand of politics ever comes back into fashion, the Tories are going to be where they were, which is flat on their backs with their feet in the air.”

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More painful has been the relentless rubbishing of the record from the left.

Ed Miliband had little positive to say about the party’s 13 years in power and Jeremy Corbyn’s leadership is predicated on the assumption that New Labour and all its works were terrible.

“The Conservatives are so much better at defending their own history,” reflects Blair, rather ruefully. “The Labour party has spent a large part of its time trashing its own record. I find it weird, the acceptance that somehow the financial crisis was the product of a Labour government. Which is completely bizarre – it was a global financial crisis that started in the sub-prime mortgage market in Florida. And then, in a much bigger way, saying New Labour basically deserted our principles … The very reason for modernising the Labour party was to make it capable of answering the challenges of the new world and a changing society. We retreated at first slowly and then with ever greater pace from that essential notion. People began to see the process of modernising as a betrayal of principle. That is always the danger with progressive parties, but it’s a particular danger in today’s world. Look what’s happened to the socialist party in France.”

Even friends say that Blair should shoulder some responsibility for the tainting of New Labour. I suggest he might have received a more sympathetic hearing had he been a more careful custodian of his post-prime ministerial reputation. He accepts this criticism. “Yeah, absolutely, and I’m not saying I haven’t made mistakes in that because I think I did.” Then he musters his defences: “I’ve actually spent the vast bulk of my time since leaving office on pro-bono charitable work in Africa and elsewhere and all I can say about my so-called wealth is the reports of it are greatly exaggerated.” He could put an end to all the conjecture by putting a number on it. Is he worth £50m? £30m? “I’m certainly worth neither of those things.” More or less? “A lot less. What is true to say: I’ve got a very nice house in London, nice house in the country, each with significant mortgages. The equity in those is the bulk of my wealth. I have given away more than I’m worth. I’ve just transferred the £10m we built in the business – this was always my intention – into the not-for-profit.” He has founded a new institute to pursue his causes and to support younger politicians.

One school of thought about Labour’s predicament says that it’s not just the Corbyn problem. It’s also down to the legacy of Blair. He is another reason that a chunk of Labour’s traditional support is off elsewhere. With his well-cut suits, his globe-trotting, his offices in Mayfair, he personifies the international liberal elite that has provoked some voters to revolt. Some critics further join dots between his government’s liberal policy on immigration and the Brexit vote. He is not having that. “Some of the first legislative battles I had were on reforms to immigration. I advocated identity cards precisely because I understood people wanted rules around immigration, and I knew that without rules there would be prejudices. So I completely get people’s concerns on immigration.

“My point on Europe is different. If we stop all these European migrants coming, we’ll just have to find a different way of getting them in because we need them for our economy. This idea that some kid from a working-class estate in the north of England is going to get a job because we stopped some guy coming and working in the hospitality sector in London, it’s just ridiculous.

“This is the tragedy. Without a strong Labour set of positions, we have Labour people contemplating voting Tory when the only impact of that is that their lives are going to be poorer and they’re going to have less opportunity.”

The psephologists, the bookies, the pundits and virtually all politicians regard this election as a foregone conclusion: all assume Theresa May will be back on 9 June. “If the polls are right, she is going to win a big majority,” Blair agrees. “If they’re right, then that’s what’s going to happen. The important thing is what’s the mandate. That’s what we’ve got to concentrate upon.”

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Some contend that it will be a double positive if May gets a thumping majority on the grounds that it will strengthen her negotiating position with the EU and allow her to face down the hardline Brexiters on her backbenches. Does Blair buy that argument? “Absolutely not,” he snorts. “It’s totally naive.” May is “in many ways a reasonable, sensible person, mainstream centre-right politician”. He’s met her privately since she became prime minister. “The trouble is, she’s a reasonable person delivering an unreasonable policy in the case of Brexit.”

“Why do you think the Ukip people are folding into the Tory party? Not because they think she’s going to deliver a softer version of Brexit. It’s because they think they’ve won. And as for strengthening her hand, the absolutely central thing to realise is she’s tied her hands by saying she’s going to get out of the single market.

“If we really do Brexit and we do Brexit with withdrawal from the single market, you can forget her ideas of a more cuddly capitalism. A low-tax, light regulation, offshore hub economy, that is where you will end up. This is the rightwing fantasy. It’s driven by the right of the Tory party and the cabal that runs the rightwing media in this country.”

He pulses with vexation about Labour’s reluctance to properly engage on Brexit. “I find it very frustrating. A lot of Labour people say: ‘Let’s just talk about the National Health Service.’ And I’m saying to them the whole time: ‘Guys, you can’t do this. You’ve got to fight a dual campaign.’ We should be educating the British people, enlightening them over the next weeks about the difference between the single market and a free-trade agreement, because there’s a reason why our currency is 15% down since the referendum result. That is the prediction of the international financial markets. That’s their prediction about our economy and our people being poorer. That is because they know we’re getting out of the single market.

“This is fundamentally about the nature of the mandate. I say to the British people: ‘Remember, this is five years of a parliament.’ Five years. So you need to work out how you hold this government to account through the most important negotiation this country has faced since the second world war and through what are going to be painful decisions around things like healthcare and education.

“You’ve got to say: don’t give her a blank cheque on Brexit, don’t give Mrs May a blank cheque on the health service and all these other things. That is, in my view, the right and the only way to fight this election given where we are now. The argument that Labour people, even if they’re Leave, will understand is the blank cheque argument.” This is a potentially potent message, but it is also one heavily freighted with the implication that Labour has absolutely no chance of winning. “For the avoidance of doubt, I’m voting Labour. I hope people vote Labour. There are masses of great Labour candidates standing and I wish them well.” There has been doubt about this because in previous remarks he appeared to advocate backing candidates, of whichever party, that were committed to resisting hard Brexit. He now insists: “I’m not advocating tactical voting.” He picks his on-the-record remarks about Labour with care now that we are in the heat of an election campaign: “I’m not getting into issues of leadership.”

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I have a go anyway. In common with every other living former Labour leader, he has previously called on Corbyn to stand down. Having been prime minister for a decade, can he hand on heart say that he thinks Corbyn is fit to lead the country? “I’ve said all I want to say on that.” Would he trust Corbyn with the nuclear deterrent? “I’m really not going to comment on that.” One last go. Does he share the view of Roy Hattersley, once the party’s deputy leader, that Labour is in a worse place than it was in 1983 when it went down to its severest postwar defeat? “Pass. Let’s move onto the next one.” “Very loyal!” I say. He laughs.

Neil Kinnock recently expressed the fear that he would never see another Labour government in his lifetime. Some go further and wonder whether Blair will enter the history books as the last person ever elected as a Labour prime minister. “Here’s what I would say about that. We mustn’t go back to where Labour got to at a certain point, after 1983, where people spoke about the Labour party outside and inside the party as if the gods had decreed that, unfortunately, there can now only be Tory governments.

“One of the remarks that really made an impact on me in the 1980s was when Michael Heseltine was asked whether Labour would win again. And he said: ‘Labour will win when it wants to.’ And I thought at the time that was a very profound remark because the Labour party can win at any point in time it wants to get back to winning ways. It’s just got to make a decision that it’s going to do it.” He is gladdened by the rise of the centrist Emmanuel Macron in the contest to be president of France. “I know him and I like him. He’s a very smart, capable guy.” Perhaps Macron, charismatic but not fully formed, reminds Blair of the younger self who swept to power in Britain in 1997. “The broad lesson is the centre ground is still strong and if you provide people with a progressive centre-ground alternative they’ll vote for it.”

When the inexperienced, sometimes callow and in certain respects naive Blair arrived in power, he appeared to think he could please all of the people all of the time. Over the past 20 years he has learnt what it is like to be widely unloved. “As your readership response to this interview will tell you, I evoke a lot of disagreement and anger. Nowadays, you stick your head out of the door and you get a bucket of something poured over you. That’s the way it is. I don’t have to do this stuff, but I’m passionate about this country. I care about this country. I find the present state of politics at one level depressing and at another level stimulating, exhilarating even, because of what’s at stake.”

Even at such an occluded time for his party, his innate optimism breaks through. “It’s certainly true we don’t have a God-given right to carry on as a competing party of government. But there’s no reason why Labour can’t become the repository of that new coalition of progressive forces that is available to us in today’s society and which is basically the same progressive coalition that brought us to power in 1997.

“For progressive politics to win, it’s got to be constantly modernising the application of its traditional values. In a world that’s defined by accelerating change, the progressives have got to be the leaders of that change. The New Labour attitude, the New Labour mindset is not just as relevant today, it’s even more relevant today.”

So says Labour’s only hat-tricker, still passionately in the fray 20 years on from his first victory.