Candidates in up to 40% of GCSE and A-level exams are being awarded incorrect grades, a study by the regulator has revealed.

In the first analysis of its kind, Ofqual has calculated the probability of a pupil getting the correct grade in “subjective” subjects like English or History as between 52% and 58%. That means more than four in ten could be incorrectly graded.

For Maths and Chemistry where examiners can be more definitive about answers, the chance of a correct grade rises to more than 90%.

Overall across the 13 popular subjects analysed by Ofqual, statisticians estimated that meant one in four grades at GCSE, AS and A-level could be incorrect because of marking inconsistencies and the design of the tests.

Ofqual maintains the quality of its marking is among the best in the world but that it is required by the government to put the “value” of qualifications ahead of “absolute reliability” of assessment that could be achieved by reducing exams to multiple choice papers.