The Headmasters' and Headmistresses' Conference (HMC) also suggested that a single examination board should be set up to administer A-levels to ensure that all students were on an equal footing.
The proposals comes a week after government advisers published a damning report on the marking of Oxford and Cambridge Exam Board English A-level papers.
Senior examiners at the board, which is used mainly by independent schools, were criticised for improving marks of candidates from independent schools.
Dr John Moore, headmaster of the King's School, Worcester, and chairman of HMC's academic policy sub-committee, said the conference "deeply regretted" the failure of the board's procedures and was anxious to avoid a repeat of the problems.
Dr Moore denied independent schools had benefited unfairly. "Whatever failures there may have been in the procedures, all candidates were affected equally, whether they were from independent or state schools."
But he acknowledged that public perception of the fairness of exams was crucially important. "Exams must be a fair process and must be seen to be fair. One way of guaranteeing that is for the candidates to be `blind' - identified simply by a number," he said.
The move would bring the Oxford and Cambridge board, which currently prints pupils' names and schools directly on to papers, into line with most other boards.
The conference also called for moves towards a single national exam board, providing there were "sufficient safeguards to ensure a range of syllabuses and to permit curriculum development".