Kenneth Clarke, the Chancellor, has warned councils to expect a standstill settlement for local government in 1997.
But local authorities, which are already spending Pounds 668 million above government estimates of what needs to be spent on education this year, claim they need an extra Pounds 535 million next year.
And the Association of Metropolitan Authorities and the Association of County Councils are putting in a bid for a 3 per cent increase, plus inflation, for education. A standstill budget for education would require a rise of Pounds 317 million, or 1.7 per cent before inflation.
Mrs Shephard won an increase in education funding this year, and authorities fear that if she does not pull off a similar trick for 1997, the consequences will be dire.
In an election year, it may be foolish for the Government to ignore the strength of feeling among parents and governors over education cuts.
John Fowler, assistant AMA education secretary, was hopeful Mrs Shephard would argue their case. He said: "We recognise Kenneth Clarke wants to screw down education, but believe the weight of parental opinion will show him there is a need to invest properly in the nation's future."
The appeal to Mrs Shephard on Monday will come just hours after the National Confederation of Parent Teacher Associations reveals the findings of a survey on the state of the nation's schools.
The survey will focus on funding, morale, class size, pupil:teacher ratios and the state of buildings, and will disclose how much cash parents are now raising to keep schools going.
Meanwhile Chris Woodhead, the chief inspector of schools, was this week criticised for the non-appearance of a planned report by the Office for Standards in Education on funding.
The Campaign for State Education said OFSTED's corporate plan had promised a report this spring on patterns of expenditure in primary and secondary schools.
Furthermore, it said the chief inspector's annual report and the press release which accompanied it had revealed plans were in hand for "an investigation into the level and distribution of resources" in schools.
OFSTED has undertaken some work on how schools manage their funding, but Mr Woodhead has told Margaret Tulloch, executive secretary of CASE:"We have not yet decided whether or when to publish our work to date."
She accused him of changing the parameters of the investigation, saying looking at how schools managed their money was "not quite the same as looking at variations in funding in different geographical areas or sectors".
In a letter to Mr Woodhead, she added: "Government frequently quotes OFSTED as an independent inspectorate, so it is essential that parents, teachers and governors can rely on OFSTED reporting everything that they, as well as government, might need to know."