They say that comments from chief inspector Chris Woodhead have undermined confidence in the local authority inspections which began at the start of the year.
In a letter sent this week, Philip Hunter, chief education officer in Staffordshire, and his East Sussex equivalent David Mallen, say that Mr Woodhead's view that local authorities should not be involved with the majority of schools calls into question his objectivity as the inspections' supervisor.
The letter will ask Mr Blunkett to point out to his chief inspector that the law requires the report on a local authority should be written by the HMI who carries out the inspection, not Mr Woodhead.
Relations between chief education officers and Mr Woodhead have not been helped by public rows over the report of the inspection of Birmingham's education service. Mr Woodhead admitted being part of the editorial team that prepared the report, but denied that he was responsible for criticising Birmingham's chief education officer, Professor Tim Brighouse, in an early draft.
Ministers will be told that Mr Woodhead's views that local authorities should only deal with poor or failing schools is not in line with the Government's plans to require them to prepare education development plans setting targets for all schools in an area.
The legislation states that the reporting of an inspection should be the responsibility of the inspector in charge of the team carrying out the work. However, Mr Woodhead claims his role as head of OFSTED gives him final editorial responsibility for all reports and that responsibility extends to reports of the inspections of local authorities.
The Government has announced that local authorities will be inspected every five years and the first 12 are under way. The Birmingham inspection was carried out before the legislation came into force.