A report on the Independent Schools Inspectorate, which monitors standards in private schools, said inspections had improved “significantly” in the past year. The ISI monitors 1,300 schools accredited by the Independent Schools Council, accounting for some 80 per cent of pupils in private schools.

As part of an annual review of ISI standards, Ofsted shadowed 22 inspections. All but two were rated “good”. It said inspection teams built up thorough evidence before making recommendations, inspections were well managed and reports written about schools were well structured and incisive. It also said heads appreciated the “courteous and sensitive” way that teams worked.

But in a fifth of cases there was a “mismatch” between the needs of the inspection and the composition of the team that led to “some lack of clarity” in feedback. It also found inconsistent use of national comparative data in assessing pupil achievement and that detail provided in boarding school inspections varied greatly.

In a separate report last year, Ofsted said a quarter of non-ISC schools failed to comply with health and safety standards, compared with only one in seven of those supported by the ISC.