Council leaders claimed Gillian Shephard's 3.6 per cent increase for schools in her "Budget for education" actually amounted to a cut of Pounds 41 per pupil.
They said they were already spending Pounds 750 million more on schools than the Government believed they should and had told the Education and Employment Secretary they needed Pounds 1 billion more next year to avoid further cuts.
Mrs Shephard told local authorities they could spend an extra Pounds 633 million on education next year - but ministers were not prepared to fund the increase through central government grant.
If education is to get extra money next year, local authorities will have to either cut other services or raise the council tax.
Graham Lane, chair of the Council of Local Education Authorities, said council taxes would have to go up by 6 per cent and the teachers' pay award would have to be kept within inflation. He said: "It is a conjuring trick, if the money is raised through council tax then the poorest sections of society will be hit. It will mean fewer teachers will be employed and the money for repairs is the equivalent of a bucket for each school to collect the drips from leaky roofs. When parents see the effect of this budget on schools they will react by voting in the general election for a party committed to education."
The Association of County Councils and Association of Metropolitan Authorities said it was clear now that class sizes would rise.
They added: "The vaunted increase for schools barely meets inescapable new commitments, such as special needs and the 1996 teachers' pay award, and does nothing to improve class sizes."
Local authorities had wanted to spend an extra Pounds 125m next year on reducing class sizes and had warned there would be severe long-term educational implications if action was not taken soon.
But while that was merely a "desirable change" they said they needed to spend at least an extra Pounds 785 million or 4.2 per cent over current spending just to accommodate additional pupils and meet statutory demands.
Spending has to increase by at least Pounds 136m to educate 54,000 more pupils who will be in schools next year and the second phase of this year's pay award will add Pounds 75m to costs.
On top of that they have to spend Pounds 20m on transport, Pounds 67m on special needs education and Pounds 43m on the nursery voucher scheme.
Vital repairs and maintenance to schools are already being neglected as headteachers struggle to balance books and avoid making staff cuts.
Doug McAvoy, general secretary of the National Union of Teachers, said: "For the Pounds 3 billion cost of repairing and replacing our crumbling schools, the Government offers Pounds 50m - this is an insult to those children faced with outside toilets, leaking roofs, inadequate facilities and dingy and unhealthy school buildings."
Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said: "Children will be paying for the penny off income tax through larger classes, unrepaired and dilapidated school buildings and missing, shared or tatty schoolbooks."
David Hart, general secretary of the National Association of Head Teachers, said schools were facing a triple whammy - the Budget, a pay award next year which Government is unlikely to fund and pensions changes.
"Is it any wonder that heads and deputies are at the end of their tethers? The Government should not under-estimate the extent of the anger felt by those responsible for management of schools."
Peter Smith, general secretary of the Association of Teachers and Lecturers, said: "Tax cuts today deny children books tomorrow. Parents would have preferred a penny more for education, not a penny less to buy votes."