Don Foster, the Liberal Democrats education spokesman, has called on her to widen the inquiry being carried out by the Funding Agency for Schools into allegations about false pupil numbers at GM schools in Hampshire.
Statistics provided to him last week by Robin Squire, education junior minister, reveal that 23 per cent more meals were eaten in GM primaries than in their local authority counterparts. In the secondary sector, the total was 27 per cent more.
The figures are included in the statistical returns that are made in January each year and used to set school budgets - county and grant-maintained.
In Hampshire education officials estimate GM schools boosted their budgets by a total of Pounds 150,000 a year while in Kent, officers estimate additional meals at six GM schools have cost the authority Pounds 32,000.
Kent is now investigating and a spokeswoman said: "There are some surprising increases. We know every year there are fluctuations but we also know the bounds of probability."
Mr Foster reminded Mrs Shephard of the importance in the calculation of an individual school's grant, of the number of school meals that are consumed on census day each January. And he asked her: "Will she condemn any school - such as the one in Hampshire - that last year urged parents to persuade children to eat a school meal on census day to boost its grant?" Mrs Shephard said the FAS, the York-based body charged with overseeing budgets of GM schools, was investigating and would comment no further.
But Mr Foster has now written to her asking for the nationwide inquiry, saying: "The financial penalties suffered by many LEAs due to additional paid meals in GM schools could be considerable."
Hampshire estimates that GM schools could have boosted their budgets by a total of Pounds 150,000. Evidence sent to the FAS by the council shows that an extra 2,541 pupils had paid meals at GM schools on census day this year.
Last year a GM junior school in the county had its budget cut after the council complained about pupil numbers.