A "staggering" waste of money has been uncovered by Sir Philip Green. Good news. The more efficiency savings, the fewer cuts threaten schools, Sure Start or home care for the elderly. Let's leave aside the tricky question of whether Sir Philip will actually succeed in saving the state more than he and his family have saved themselves in avoiding taxes in Monaco: in one year alone – 2005 – £1.2bn was paid to his wife, avoiding British tax. Let's look instead at the meaning of the waste he has uncovered.

He has not delved into the public services, but has confined himself to the hardware. Not one job would be cut by implementing his ideas, he says reassuringly. His short and impressionistic report only takes a snapshot of some spending: he warns that there is "no total number" for savings. Examining the management of property and the procurement of goods, services, IT and telecoms he finds it chaotically under-centralised. What's more, he complains, there is "no reporting and no accountability" at the centre.

His examples of crazy variations in cost range from a box of paper costing £73 in one department and just £8 in another. Coffee varies from £1.45 to 90p, identical laptops from £2,000 to £353. Property is often wastefully mismanaged. But an example of good purchasing has been in energy, where four years ago the £2.8bn government spend on gas and electricity was mostly centralised, resulting in a saving of £500m. We need a lot more of that, he says.

How painless and sensible if all this waste can really be eliminated. Doubts arise because all governments summon private sector magnates to scour the corridors of power for magic savings. In 2003 Sir Peter Gershon, Labour's waste-buster, found billions lying around. As a result Labour demanded annual savings of £35bn, ordering a yearly cull from every Whitehall department and local authority. It was not easy to do, nor was it done.

In July the National Audit Office examined the results: every government department claimed it had made the requisite savings – but had they really? The NAO concluded that only 38% of reported savings were definitely achieved, while there was doubt over a further 44%, and 18% of claimed savings were rated in the "red" zone – as over-stated or non-existent. That shows just how difficult it is and how hard every government must keep trying.

Most of Green's savings had already been identified by the NAO, which made similar recommendations to the new government: national joined-up procurement, using the mighty weight of government credit rating to strike the best deals with manufacturers, services and landlords. It's not rocket science – it's blindingly obvious that desks, computers, office space or paper clips will be cheaper if centrally purchased.

How did this government respond? By ignoring the NAO altogether and haring off in entirely the opposite direction. Why? Because the very idea of joining up, co-operating, collaborating, and centralising is ideological anathema to them. Francis Maude, Eric Pickles, Michael Gove, Andrew Lansley and the other ideologues-in-chief have devoted all their efforts to reorganisations and quango culls designed for extreme decentralisation.

Everything they have said about "no top-down direction", "local control" and "local accountability" means devolving power and removing central regulators and auditors; last week even the body overseeing fair play in the energy sector was abolished, leaving each consumer to sort out the rogues from the honest suppliers. The hope is that ministers at the centre will no longer be blamed for anything. "Devolving the axe" looks like a tempting, if overoptimistic, way to escape public anger over local cuts.

The idea is that citizens will monitor public services themselves, with local politicians answerable only at the ballot box for the effectiveness of their services. But how can patients or parents detect best value in the buying of syringes or school chairs? The ideology demands the NHS, schools, social services and almost everything be devolved, often beyond the control of local councils, to lowest possible levels of decision-making. No more auditors and regulators to compare value for money. All this tugs embarrassingly in the opposite ideological direction to Green.

Take just one example: the very first quango the coalition axed was Becta, the clunkily named British Educational Communications and Technology Agency. It's easy to imagine Michael Gove, newly arrived in his education department eager to swing his axe, turning up his nose at its rather mushy self-description: "Becta leads the national drive to inspire and lead the effective and innovative use of technology throughout learning." Off with its head! Oops ... actually what it does is procure the best computers and programmes for schools as effectively and cheaply as possible, in exactly the way Sir Philip Green says all departments should.

Once it has gone, all headteachers will be on their own, thumbing through brochures, subjected to marketing calls from sales reps trying to bamboozle them with gizmos and super-new electronic teaching aids that may be the best or the worst. Even if teachers succeed in choosing the best, they will get the worst prices without mass purchasing. Academies and free schools will be on their own, as will free-standing hospitals and GP consortiums – all in hot competition with one another, overseen by the hospital regulator Monitor, charged with ensuring they compete, not co-operate.

Green's report seems entirely non-political, and he seems unaware of the impossible contradictions he has landed on the government. To him this is just plain business sense: the government is one entity, national and local. For maximum efficiency it should behave like one entity. Individualistic localism and fierce competition between its components are simply not compatible with the idea of efficiency he expects from a single enterprise, with a single united objective – to produce the best services possible for the cheapest price.

So, will we see Francis Maude in the Cabinet Office doing a U-turn to co-ordinate and regulate all government, or will the ideologues-in-chief go on with their programme of fragmentation and competition while this report gathers dust on a shelf?

The Verdict: Did Labour Change Britain?, by Polly Toynbee and David Walker, is available from guardianbookshop.co.uk