Headteachers have expressed their dismay that the Department for Education and Ofqual are "intent on blaming each other" for the summer's grading fiasco.
The Association of School and College Leaders' general secretary Geoff Barton has also urged the government to develop contingency plans to cope with Covid-19 disrupting next year's exams.
He was responding to comments by schools standards minister Nick Gibb during education questions in the House of Commons today.
Mr Barton said: “We are increasingly concerned that we are no closer to understanding what went wrong with this year’s GCSE and A-level grades, and that lessons have not been learned.
“Schools minister Nick Gibb says Ofqual assured the government that the model for standardising grades was fair.
"Last week, Ofqual chair Roger Taylor told the Education Select Committee that Ofqual advised the government about the risks associated with this approach from the outset.
“It seems that Ofqual and the government are intent on blaming one another. Students, parents, schools and colleges all deserve clarity about what happened, and we once again call upon the government to commission an independent review."
This summer's GCSE and A-level grading was originally done through a moderation process in which Ofqual took into account centre assessed grades (CAGs) submitted by schools, a pupil's ranking in each subject at their school and the school's past performance.
However, this was abandoned in a major U-turn after A level results were published and there was an outcry at the way in which grades submitted by schools had been downgraded.
Instead, students received whichever result was higher: the centre assessed one submitted by schools or the moderated Ofqual grade.
Mr Barton has also raised the question of what will happen in 2021 with exams.
He added: "More worryingly, Ofqual and the government now appear to be pinning all their hopes on students being able to sit a full set of exams next year, despite the evidence we have seen in the first few days of term that there is likely to be ongoing disruption because of coronavirus.
“The grades fiasco that took place this summer should surely serve as a stark warning about the difficulties if students are unable to take exams.
"And yet, there is no back-up plan if exams cannot be taken, or if the preparation of students is significantly disrupted.
“It is imperative that the government and Ofqual act swiftly to put in place a robust contingency plan before time runs out.”