For at least two decades Margaret Thatcher haunted the Conservative party. The guilt over her regicide, the fear that they would never find a leader to match her, the urge to do her will by distancing Britain from the hated European enterprise – one way or another, the Thatcher ghost refused to rest. Perhaps David Cameron’s unexpected success on 7 May will allow an exorcism of sorts, but her shade still lingers. The coming referendum on Europe will, for many Tories, carry a spectral echo of her famous battle cry: “No. No. No.”

Labour is similarly haunted by its own three-time election winner. But there’s a big difference. While Tories feel a collective guilt at getting rid of Thatcher, Labour can’t quite accept that it ever made Tony Blair its leader. It’s not the 2007 toppling of Blair that preys on its mind, but his 13 years at the top. The Labour tribe doesn’t know what to make of Blair, whether to revere him for scaling the electoral mountain three times or to revile him for what he did once he got there.

Labour needs to separate what Blair got right from what he got wrong, to hold on to the one while discarding the other

The evidence is apparent in the current Labour leadership campaign. For one camp – Chuka Umunna, Liz Kendall, Alan Johnson, Blair himself – the election defeat prompted an obvious conclusion. Labour had lost because too many people rejected it in favour of the Conservatives. It ought, therefore, to draw once again from the Blair well, and persuade middle-class people with ambition that Labour speaks for them too.

But the response to that idea was telling. Diane Abbott tweeted: “‘Labour must return to “aspirational Blair years”, say senior party figures’ Together with illegal wars?” For Abbott, “aspiration” was code for the invasion of Iraq. Never mind that the two are unconnected. “Aspiration” has taken its place alongside “wealth creation” or “modernisation” as a trigger word – one that, as my colleague Rafael Behr wrote this week, instantly evokes the most despised aspects of the New Labour era: “The City, privatisation and war in the Middle East – prongs on the trident of demonic ‘Blairism’.”

This makes debate difficult. If Labour cannot talk about one thing without setting off psychological associations with another, then it cannot get to grips with either its recent past or its possible future. Kendall may well be felled by this problem, the Blairite tag around her neck choking her.

For some, the word itself is radioactive, contaminating Kendall’s candidacy regardless of what she actually says. In this climate of code words and presumed factional allegiances, it has come to the point that to suggest Labour needs to win seats in the south of England is to identify as a Blairite and therefore as a neocon warmonger and apologist for corporate greed.

The root of this problem is Blair himself, or rather Labour’s relationship with him. The task now is for Labour to place itself on the couch and sort this out, once and for all. It will require the primary task of all analysis, which is the making of distinctions. Labour needs to separate what Blair got right from what he got wrong, to hold on to the one while discarding the other.

That sounds straightforward, but too many in Labour can no longer even see the credit column in the Blair ledger. Perhaps this month’s defeat will make it more visible. Put simply, Labour almost always loses. Over the long last century, a Labour victory has been the rare exception not the rule. Only two leaders before Blair had ever won a parliamentary majority. Labour had never – not once – served two full consecutive terms in office. So to win three full terms was a staggering achievement.

When one gazes at the task confronting Labour now – the apparent impossibility of winning seats in the English north and south, both in the market towns and the suburbs, as well as in Scotland – it is remarkable to recall that Blair made it look easy. Somehow Labour has to learn from that experience. Yes, things were so much easier in Blair’s heyday, facing a clapped-out, discredited Tory opponent and operating in a world all but free of the SNP and Ukip, where Labour had the battlefield all to itself. But still Blair did what no Labour leader had done before or since. It’s surely worth remembering how he did it.

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Of course there is much Blair got wrong, with Iraq seared into place at the top of that list for evermore. But the mistake is to assume that, say, foreign adventurism was logically inherent in Blairism from the beginning. It wasn’t. On the contrary, Blair’s stubborn conviction on Iraq came as a surprise to both his party and the electorate: funny to recall now, but early Blair was mocked as a telegenic empty suit with no beliefs at all. In the end, it was an excess of conviction, not a lack of it, that undid him.

The point is, there is much in the Blair record that can be rejected without throwing out his key insights. The first was his recognition, together with Gordon Brown, that Labour would not even begin to get a hearing until voters felt able to trust the party with the economy. That was the sine qua non. A reputation for economic incompetence was why Labour had been exiled from 1979 to 1997 – and it is why Labour will remain in the cold from now until its reputation is restored.

Blair also understood that a vote is not an act of charity. Voters may be moved by stories of those at the sharp end – on zero hours or paying the bedroom tax – but the majority, especially those who are in work and own their own home, will vote for the party they believe will maintain or improve their own lives. Blair positioned Labour as a party that was determined to help not just the neediest, but to help you too.

None of this means reheating Blair’s specific policy prescriptions, some of which were designed 20 years ago for what was a very different world. Too many Blairite ultras are guilty of that error, treating his programme as holy writ whose every detail must be followed even now. (Private-sector provision in the NHS is an example.) As Blair of all people understood, political parties die when they become enslaved to a dogma. The trick is to retain the underlying ethos and adapt it to today.

This is Labour’s task now. Strip out what was wrong, including what was morally wrong; junk what is out of date; and take a cold, clear-eyed stare at the Blair legacy. That will include much of the New Labour record – the minimum wage, the pensioners lifted out of poverty, the civil partnerships, the Sure Start centres, devolution, the windfall tax, the rebuilding of broken schools and rundown hospitals – all of which is too often forgotten. But it will also mean working out how Blair persuaded a country that doesn’t often vote Labour to elect three Labour governments on the trot.

Make no mistake, Labour doesn’t need to do this for Blair’s sake: he can take care of himself. It needs to do it for its own sake. Until Labour gets over its Tony Blair problem, it will remain out of power – unsullied perhaps, but utterly impotent.