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Mr Balls's announcement comes after he received heavy criticism from Local Education Authorities (LEAs) and schools for springing last month's announcement on them that a significant minority were breaching rules without saying how many.

The Government's research methods were also questioned after Mr Balls admitted at the time that his department’s survey was “unverified desk research”.

Local authorities, furious at being given only one day’s notice of the investigation, challenged its findings. Bosses claimed that schools were not contacted and much of the information was gleaned from prospectuses and websites, which may not have been updated to conform with the new admissions code.

In a separate document which was published to advise parents, the Department for Children, Schools and Families set down rules which schools must abide by.

The document says state seconary schools must:

- admit everyone who applies if there is space

- give priority to children in care

- use a fair, "tie-breaker" system if many children fit the same criteria.

Under the system, they must not:

- interview children or parents

- only consider an application if the school is a parents' first preference

- take into account the behaviour of other family members

- use selective tests

- ask for photographs of, or ask for extra information about, pupil

- ask for fees, even if they are being demanded as 'voluntary contributions'.

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