They have published a report saying the results of the IGCSE in English language were flawed and pupils received unfair grades.
The exam board, Cambridge International Exams, said it was “confident” in the accuracy of the results.
Exam regulator Ofqual said the exam results were reliable and pupils had received “appropriate” grades.
The Headmasters’ and Headmistresses’ Conference (HMC) and Girls’ School Association said an “unprecedented number” of schools had come forward with concerns about the results.
The report said the exam results “cannot be trusted” and there had been a “large-scale award of false grades” for the IGCSE English language paper taken by pupils in May 2015.
‘Out of line’
The independent schools’ groups said there had been problems with the grade boundaries and the results had been “exceptionally out of line” with expectations, with pupils forecast to get top grades receiving U grades.
Leicester Grammar School headmaster Chris King, who chairs the HMC, said they were publishing the report after months of “fruitless formal appeals”.
“Yet again, schools have known that students have been graded unfairly but have been unable to gain justice for pupils under the current system,” he said.
But the claims about the IGCSE were strongly rejected by the exam board.
Roderic Gillespie, director of assessment at Cambridge International Examinations, said the independent schools’ report was “flawed” and had been based on a “small sample of self-selecting schools unhappy with their results”.
“There is no evidence in the report to justify re-grading the exam papers,” he said.
Ofqual said it had checked the schools’ claims but remained unconvinced by the evidence.
“It is unreasonable for any study to make assertions about an entire cohort of students based on the results of an unrepresentative sub-set of schools,” said an Ofqual spokesman.
The exam watchdog said it was “satisfied that the grade boundaries were suitable”.
Last year saw a record number of grades being changed after pupils appealed against results.
There were more than 90,000 GCSE and A-level grades changed in 2015, almost twice as many as three years before.