Effective and efficient authorities will be identified by the Government in order to act as benchmarks for the rest.
The intention is to clarify and regulate the financial basis of local management of schools, dispersing the "funding fog" criticised by the School Teachers' Review Body as being impenetrable to most teachers and governors.
The Government has promised to ensure that 90 per cent of every LEA's schools budget is actually delegated to the schools - but has discovered that there are wide variations in what goes into the schools budgets in different authorities, and the amount held back for administration.
Mr Blunkett said: "We're committed to devolving a greater part of the budget, but you reach a situation where you're addressing only a proportion of the totality rather than the whole.
"We need to examine what it is that authorities are currently doing with the amount that is held back. It does vary depending on the range of services they provide. Some are providing adult education; others are providing high quality educational psychology services; some include the youth service within that hold-back budget element."
The "crunch issue" is how far administrative costs affect the amount which is withheld from the schools, he said. This can vary from 13 per cent to 30 per cent of the total.
"We need to examine with them exactly why that is the case, " said Mr Blunkett. "We need to benchmark the best practice within LEAs so that we can say: 'Look, if this authority can deliver a high quality service with this proportion of its budget retained, then why not other authorities?'
"We want to explore what the true costs are of delivering core services. That will give us the opportunity of a complete revision of what is included in the delegated budget and what is included in the held-back part of the schools budget - so that we are clear what it is that is going into that, and what is being shunted out".
The review will reveal differing practices, and could well free more resources for direct provision of educational services, which will be necessary if LEAs are to perform the enhanced role intended by the Government in the delivery of higher standards in schools. Mr Blunkett is considering setting spending targets for administration costs, perhaps at #163;50 per pupil.
The evaluation will be carried out "as a joint venture" by the Audit Commission, along with the Department for Education and Employment, the Local Government Association, and the LEAs themselves.
The Audit Commission has also been asked to carry out a wide-ranging review of the role of local education authorities, and their efficiency and effectiveness, which would feed into the financial inquiry.
The signals are that LEAs are the partners of central government once more - though with a role more tightly defined by Government policy.
Some Conservative-run LEAs such as Hampshire and Cambridgeshire are responding to the new climate by increasing their education budgets by unprecedented amounts.