There is “no evidence” that the system for awarding GCSEs and A-levels this year systematically disadvantaged poorer pupils or those with protected characteristics, an analysis by Ofqual has found.

But 6,300 GCSE entries, most of them from private schools, may have received “disproportionately overestimated grades”, the exams regulator said.

Ofqual has published a technical report with in-depth analysis of the grades achieved by pupils of different genders, ethnic backgrounds, special educational needs status and free school meals eligibility.

The analyses aimed to examine “concerns” that the system used this year could have introduced new inequalities, or affected pre-existing ones.

It concluded that there was “no evidence that either the calculated grades or the final grades awarded this year were systematically biased against candidates with protected characteristics or from disadvantaged backgrounds”.

Exams were cancelled this year after schools closed to all but the most vulnerable pupils and the children of key workers in March.

Instead, schools were asked to provide centre-assessment grades and a rank order of pupils within each grade, which were then standardised by exam boards using a computer algorithm.

But the government was forced to U-turn and issue non-standardised centre-assessment grades after an outcry over the calculated grades, around 40 per cent of which had been downgraded at A-level.

An interim report, published on A-level results day, showed that pupils from low socio-economic backgrounds saw a greater drop in A* to C grades than those from medium or high socioeconomic backgrounds.

Ofqual subsequently clarified that although poorer pupils saw a bigger drop in grades B to E as a result of standardisation, the proportion achieving A* and A grades actually fell by less than it did for pupils from better-off backgrounds.

The new report looked at the centre-assessment grades, calculated grades and final grades issued to pupils

It found that had calculated grades been issued, the results “would have been more closely in line” with the established relationships between student characteristics and outcomes seen in previous results.

However, the changes seen by using final grades were “small”.

There was “some evidence” that around 6,300 GCSE entries by pupils with low prior attainment and unknown socioeconomic status “may have received disproportionately overestimated grades”.

Most of these pupils are at independent schools, Ofqual said, and the effect was “equally noticeable in grades using CAGs, calculated grades, and final grades”. 6,300 entries represents around 2.4 per cent of all GCSE entries from private schools this year.

In the report, Ofqual said its analyses were “clear” that the “most consistent and significant effect” of CAGs and final grades was “an uplift in outcomes”, which was not seen in calculated grades.