A rescue package worth pound;180 million is to be shared between 49 cash-strapped local authorities.
The Government this week announced the extra support - targeted at councils struggling to balance schools' budgets - as part of funding plans for next year.
All local authorities will get at least 5 per cent extra for schools next year with some receiving 6.5 per cent or more. The Government estimates that schools' additional costs will be equivalent to 3.4 per cent. All schools with static rolls should receive at least 4 per cent and most will get more.
The local education authorities getting the extra help are those receiving the lowest rises in other grants. Although this includes a third of LEAs, several that have complained of severe deficits will miss out, including Barnet, Surrey, and the East Riding.
The targeted authorities will receive a share of pound;120m next year then approximately pound;60m in 20056. Charles Clarke, Education Secretary, said an authority would only receive extra cash if he was convinced it was making every effort to support schools from existing resources.
The councils will have to produce a credible plan to balance school budgets by 20067. The greatest sum will go to Kent, one of the largest LEAs, which will receive pound;12.8m next year.
Mr Clarke said it would mean it should not be necessary to raise council taxes to pay for education.
Other councils will be able to apply for special grants of up to pound;300,000, or 0.2 per cent of their annual education funding, if they can put forward a compelling argument that more money is needed "to avoid real damage to children's education".
Ministers also pledged that:
* regulations will be introduced to ensure LEAs' spending on central budgets rises no faster than their spending on schools;
* the school standards fund and standards grant, will be increased, to pound;435m in 20045 and pound;520m in 20056;
* the management consultancy KPMG will work with the National College of School Leadership to develop guidance for schools on managing budgets. This will be available from next year, priority will go to the targeted authorities.
Croydon Council, one of the 49 authorities, said its extra pound;2.6m would make it much easier for schools to cope over the next two years.
Louisa Woodley, the council's education spokeswoman, said she was pleased the Government had "acknowledged the pressures".
Surrey's LEA will not get any extra money even though 66 of its 414 schools have deficits totalling pound;7.5m. Council leader Nick Skellet said that the most needy schools would suffer the most.
East Riding said the funding plans did "little to address the serious shortfall" in its authority.
In Barnet, also omitted, 10 heads have written to the Prime Minister warning that they face combined budget shortfalls of pound;2m. They have threatened to close their schools in the new year, when they expect this year's cash to run out, rather than lay off staff.
A Barnet Council spokesman said it was too early to assess the impact of the announcement, but said it remained "very concerned about the funding position".
Graham Lane, chair of the Local Government Association's education committee, said that, although budgets would still be tight, the settlement was reasonable and would make it easier for schools to plan. "It does look as if, with careful budgeting in schools, we ought to be able to manage satisfactorily," he said.
The 49 LEAs getting extra support are: Camden, Hammersmith amp; Fulham, Kensington amp; Chelsea, Lambeth, Lewisham, Tower Hamlets, Barking amp; Dagenham, Bexley, Bromley, Croydon, Enfield, Haringey, Havering, Newham, Redbridge, Richmond-upon-Thames, Sutton, Waltham Forest, Knowsley, Liverpool, Wirral, North East Lincolnshire, Bedfordshire, Buckinghamshire, Milton Keynes, Dorset, Bournemouth, East Sussex, Brighton amp; Hove, Hampshire, Portsmouth, Southampton, Leicestershire, Slough, Plymouth, Torbay, Essex, Southend, Thurrock, Kent, Medway, Hertfordshire, Isle of Wight, Lincolnshire, Norfolk, Oxfordshire, Somerset, Suffolk, and West Sussex.