About some things, Tony Blair might not be the ideal person to approach for advice, especially at the fee level he charges. How to conduct wars in the Middle East. How to control your chancellor. How to burnish your post prime-ministerial reputation. But on one subject he has an excellent claim to be an expert. When it comes to how to win power, you’d think contemporary leaders might think the former prime minister worth paying a little heed to.

He was Labour’s most electorally successful leader and by a long way. He took a party that had lost four elections in a row and turned it into a winning machine that secured three consecutive terms. He is one of only two people to have achieved triple back-to-back election victories since the introduction of universal suffrage. His fellow hat-tricker was Margaret Thatcher and his aggregate parliamentary majorities were larger than hers. He won his party 13 continuous years in office. That is not only the longest period of Labour government ever, it is the longest stretch of non-Tory government since 1762. I am aware that I’ve pointed this out before. I draw it to your attention again because it is such a jaw-dropper of a fact.

He presided over the most sustained economic growth in British history and at a time when other major economies tipped into recession. That was accompanied by stealthy but significant redistribution towards the less well-off while record sums were poured into public services. It is too easily forgotten how tattered was the state of the public realm back in 1997 when schools had roofs that let in the rain and the hospital building stock was in the advanced stages of decay. The current squeeze on public services would have been felt that much harder had the Blair governments not invested heavily in improving the social fabric.

Of course, his original election-winning coalition shrank over time. The laws of political entropy and his own mistakes saw to that. When he left office in 2007, pollsters nevertheless reported that a chunky majority of voters thought he had been a good prime minister overall and most also regarded him as “likable”. Not a bad result for a man who had been at the top for more than a decade and led his country into a highly divisive war in Iraq on a false prospectus and with a calamitous aftermath. Whatever he got wrong, he must have been getting something right.

Once the most popular prime minister ever, today you can regularly read that he is “the most hated man in Britain”. While probably true if your only sample of opinion is postings on the internet, where frothers of the left and right briefly pause from gobbing at each other to agree that they all loathe him, I suspect the wider, more apolitical public take a more complicated and ambiguous attitude towards him.

Unconfident about how to have a voice in domestic British politics, the past master of communication has largely stayed shtoom about it. That has made it easier for others to rewrite his history and their own parts in it. Tories now dismiss the prosperity and investment of the New Labour period as an illusion built on debt. They conveniently forget that they were so cowed by him that they felt compelled to sign up to Labour’s spending plans and David Cameron used to go round proclaiming himself “the heir to Blair”.

We would expect Conservatives to vilify the record of the last Labour government. What’s done more damage to Labour’s cause is that too many of its own people have also treated their longest period in power as an aberration. Ed Miliband has given the impression that he regards everything about New Labour as an embarrassment and Mr Blair as the black sheep of the family that no one speaks about. Mr Miliband was bound to put distance between himself and some of the unpopular legacies, but suggesting that he thinks the entire period was one epic mistake has prevented him from taking ownership of New Labour’s achievements and what was admired about them.

As his record has been trashed by Tories and repudiated by the leadership of his own party, Mr Blair has bitten his tongue. So on the rare occasions when he does make an intervention, it is bound to be news. His recent remarks to Anne McElvoy of the Economist were really very mild compared with the way in which former leaders have often talked about their successors. He made the observation that Labour had to be careful that the next election was not one “in which a traditional leftwing party competes with a traditional rightwing party, with the traditional result”. Asked if that means a Tory victory, he responded: “Yes, that is what happens.” When this was translated into headlines that he fears Ed Miliband is too leftwing to win, Mr Blair protested that he had been “misinterpreted”. I am not sure what alternative conclusion he thinks we should draw from his words, especially when he also said: “I am convinced the Labour party succeeds best when it is in the centre ground.”

To that gently expressed advice, the response from his party has been, from Mr Blair’s perspective, rather depressing. Lucy Powell, the vice-chair of Labour’s election campaign, dismissed him as a politician “from another era”, as if talking about some long-dead Tudor monarch rather than her party’s most prodigious winner. Neal Lawson, chairman of the leftish pressure group Compass, opined that the problem with New Labour’s victories was that they were “too big” and “the wrong people were voting Labour”. That is the sort of tribal ghetto mentality that Mr Blair set out to eradicate from his party. If he was about one thing, it was challenging those on the left who think it better to attract support only from “the right kind of voter” and be out of power rather than win in order to be able to do things for the people and causes you care about.

As we get into a long, nasty and brutish election campaign, the key question is whether Mr Blair is right. Are elections still won on the centre ground? And if they are, where is that turf these days? This gets to the essential nub of the difference between Mr Blair and Mr Miliband. The latter believes that the financial crisis changed the paradigm of politics. The Great Crash was also a Great Shift that opened up space for Labour to offer a prospectus that is more challenging to concentrations of wealth and power than New Labour dared to be. Mr Blair thinks that the centre hasn’t really moved in the way his successor assumes. This also sets the former prime minister apart from the man who once claimed to be his heir. The opening shots of the battle confirm that the Tories assume that the country has shifted to the right and that it is now an election-winning proposition to promise unfunded tax cuts for the affluent and a squeeze on public provision so severe that even the most rightwing of their Lib Dem coalition partners are condemning it as ideologically driven savagery.

In the current volatile climate, it is harder than usual to discern where the centre of gravity of British politics truly lies. The financial crisis, and its aftermath, has driven voters to the left on some issues and to the right on others. But my hunch is that Mr Blair is essentially correct when he contends that voters still “group around the centre”. Most people are not tribally Labour or tribally Tory or tribally anything. They have a traditionally British wariness of ideological zealotry – and often with good reason. The appeal and the animating idea of Blairism was that voters look for a government that they can trust with both the economy and with public services, which is both fair to the underprivileged and a friend of aspiration. They also look for a national leader, which Tony Blair was at his best, who can invest the country with a bit of uplifting optimism and a sense of unity rather than constantly telling everyone who they ought to hate and that everything is awful.

Today there is a Blair-shaped vacuum in British politics. Both Ed Miliband and David Cameron agree that the centre ground still exists, even if they dispute where it is. Both will campaign claiming that they represent the mainstream majority. Their dismal poll ratings tell us otherwise. Tony Blair won his first election victory with 43% of the vote. He secured his third with 35%. That seemed an unimpressive way to win at the time. Now 35% represents the peak of the ambition of both parties. Neither thinks they have a hope of attaining 43%. Whoever becomes prime minister in a few months’ time, no one imagines it is going to feel like that May Day in 1997 when New Labour came to power.

It could be that the Blair way of winning is simply unrepeatable for the foreseeable future. The electorate has become too fragmented, alienated and cynical. Times are too tough.

There may be something in that. But we should also note that this is a mighty convenient excuse for the failure of the present generation of leaders to appeal widely in every part of the country. The more they badmouth Tony Blair, the more I suspect that they are jealous of him.