Did Labour's social policy work? The answer is a pretty resounding yes, according to the LSE's definitive survey of the Blair-Brown years: "There is clear evidence that public spending worked, contrary to popular belief." Nor did Labour overspend. It inherited "a large deficit and high public sector debt", with spending "at a historic low" – 14th out of 15 in the EU. Labour spending increased considerably, but until the crash was still "unexceptional", either by historic UK standards or international ones. Until 2007 "national debt levels were lower than when Labour took office".

But the Tory myth has taken hold: Labour squandered vast sums on wasteful programmes that didn't work. Benefits were "thrown at" the idle instead of changing lives. All this is refuted by a wealth of statistics from Professors John Hills and Ruth Lupton and others in their reports on health, education and inequality. Reading this monumental research – Labour's Social Policy Record: Policy, Spending and Outcomes 1997-2010 – you can only wonder at how badly Labour has defended its record.

Labour's extra spending went mostly on improving services – hiring doctors and nurses, more and better qualified teachers, rebuilding leaking schools and aged hospitals, free nurseries and 3,500 Sure Start centres. Too few homes were built, but 90% of social housing was brought up to "decent homes" standard, rescuing estates from chronic disrepair. The gap in infant mortality rates between manual workers and the whole population closed by 10%. Education results improved markedly, with the gap in GCSE results between social classes beginning to narrow.

Cast your mind back to the heady days after the 1997 election. After years of neglect, Labour inherited a public realm in decay, squalid public buildings and neglected human lives that formed a social deficit as expensive as any Treasury debt. Ministers brimming with optimism set about rooting out the causes of poverty. Tony Blair set up the social exclusion unit inside No 10. "Social exclusion" signified not just poverty, but its myriad causes and symptoms, with 18 task forces examining education, babies' development, debt, addiction, mental health, housing and much more. Policies followed and so did improvements. John Prescott's department published an annual Opportunities for All report that punctiliously monitored these social targets: 48 out of 59 indicators improved.

So when Iain Duncan Smith or Nick Clegg sneer that all Labour did was give tax credits to lift families just over the poverty line – "poverty plus a pound" – they lie through their teeth. Contrary to Tory claims, benefits were not Labour's main instrument of social change: the benefit budget fell as a proportion of spending, outstripped by increases in health, education and other social services.

Things got better with money mostly well spent. But inequality targets were missed by miles. Everyone's health and longevity improved, with exceptional heart and cancer results, but the gap between rich and poor widened: health reflects lifetime social status more than last-minute NHS repair. In education those with five good GCSEs rose from 45% to 76% (and no, grade inflation couldn't explain such a big step up) - but the number of Neets (not in education, employment or training) rose too. And while the numbers of school-leavers getting into university reached 46%, working-class students increased only by 3%. The UK didn't, as alleged, slip down international league tables in health or education, but nor did it rise.

As for inequality itself, Blair and Brown never promised to cut it: it stayed "broadly flat". Despite the minimum wage, pay inequality worsened and the regional gap got no better. Top earnings were let rip, so overall inequality didn't budge.

Though missing an eye-watering target to halve child poverty by 2010, Labour did manage a third, while pulling most families at the bottom closer to the middle, with nearly a million fewer poor pensioners. But the working age poor without children were allowed to fall back, to be spurred into work with "a hand up, not a handout".

Professor Hills and his team will repeat this invaluable audit in January 2015. The signs are that Labour's years of social progress will hurtle into reverse – in the NHS, in poverty, in opportunities. The ill-effects in education from such disasters as the huge cut in Sure Start and childcare may take longer to emerge. But moving backwards on just about every social measure looks inevitable: the coalition's "more for less" will be exposed as pretence.

There are deep lessons here for Labour. First, it has failed miserably to blow its own trumpet. Victors usually write history, so where is Tony Blair to tell of all he achieved and rebut the mendacious narrative of the coalition?

A deeper lesson goes to the heart of the Blair-Brown years. They did all this good mostly by stealth, unsure that social programmes aimed at the poor would win re-election. They walked the walk, but talked the talk only to the party faithful. This government gets away with demolishing what Labour did because the social democratic idea behind it was never embedded in the national psyche.

The only place to cement social change is in the hearts and minds of voters. Blair and Brown were defeatists, convinced Britain was essentially conservative, individualist, imbued with Thatcherism. Confronted with the Mail, Sun, Times and Telegraph, the culture looked immutable, a force to be appeased. Not even when ordinary living standards plummeted as banks were bailed out did Labour seize the chance to make a stronger social democratic case. Ideas matter. Had Labour changed the political climate (as Cameron briefly thought), this government could not dismantle the social state. But like tumbleweed, Labour policies put down no roots to anchor ideas of collective provision and social protection.

Tories and their commentators roistered with delight at the non-shambles of Osborne's spending review. They had thought another deep cut was risky – but read Michael Portillo in the Mail, Janan Ganesh in the FT or MP Dominic Raab's new cuts plan, and they think nothing can stop their axe felling the timbers of the state in Whitehall and in town halls. History is their weapon: they get away with it only if people believe Labour grossly overspent and left nothing to show for it. This report is valuable solid evidence to the contrary.