She has told Tory and Labour MPs in Devon, where the authority is fighting a Pounds 4.4 million cut, that education junior minister Robin Squire will meet council representatives.

Her offer of help, just days before yesterday’s local government elections, is seen as a further sign of her department’s nervousness at the impact of spending restrictions on school budgets. The Department for Education has no control over local authority spending, which comes under the remit of the Department of the Environment.

Despite repeatedly claiming that this year’s settlement was “tough but manageable”, Mrs Shephard has been fighting Cabinet colleagues for more cash. In a private letter leaked to The TES earlier this year she predicted thousands of job losses and increased class sizes would result from an inadequately funded teachers’ pay settlement.

Seven councils - Somerset, Devon, Gloucestershire, Shropshire, Barnsley, Newcastle and Sheffield - have defied Government spending limits and all met this week’s deadline to submit appeals to the DoE for their budgets to be increased.

Mrs Shephard’s latest hint came in a letter to Devonport Labour MP David Jamieson.

She said capping was necessary to ensure councils played their part in the restraint of public expenditure but added: “If they choose to challenge the cap, Robin Squire would be willing to meet representatives of the LEAs in order to hear their case as it relates to education.”

The Local Government Information Unit claimed this week widespread redundancy and education cuts could be avoided in Devon for 22p on council tax bills per week.

An examination of the Government’s suggested budget cuts showed that most Devon families would actually save less than 22p a week. For most families in Somerset it would be 28p a week and most Gloucestershire families would be just 37p a week better off.

Judy Mallaber, LGIU director, said: “The cost of avoiding further difficulties for schools in these areas is very small - especially when you consider that to make up for cuts many schools will be asking parents to make more and more contributions towards the cost of educating their children.”

Council leaders in Barnsley, who want to spend Pounds 3.1 million above the Pounds 150 million limit allowed by Government, and Newcastle, which is prepared to exceed its budget by Pounds 2.3 million, have already presented their case in person to civil servants at the DoE.

The five other authorities hope to meet civil servants later this month.

Gloucestershire wants to spend Pounds 4 million above its Pounds 300 million limit, while Sheffield is appealing for an increase of around Pounds 3. 6 million, Somerset Pounds 2.6 million and Shropshire Pounds 6 million.

If the rebel seven’s budgets are raised they plan to spend much of the cash on stemming teacher redundancies, which have the knock-on effect of increasing class sizes.

DoE officials gave no indication when a decision on the appeals would be reached.