Chief executive of the Grammar School Heads Association Mark Fenton has said the A-level results had been unfair to some of its students.
He told the BBC that “a great injustice has been done” with “utterly baffling” results for some students.
He said the “only fair outcome” available would be to revert to the grade predicted by teachers and for the limit of 5 percent extra university places in England to be lifted.
The cap on increasing student numbers for each university was put in place by ministers to prevent academically selective universities recruiting heavily to make up for a fall in international students.
“Natural justice must surely now trump the understandable desire to maintain national standards in this, the most exceptional of years,” Fenton added.