Geoff Barton from the Association of School and College Leaders (ASCL) told The Independent the government “needs to show a greater sense of urgency” on the matter.
On Monday, five education organisations put forward a series of proposals over next year’s exams, including having contigency plans if pupils cannot take exams or their preparation was badly disrupted, and giving students more choice over what questions to answer.
The group – which includes the ASCL and the school leaders’ union NAHT – also suggested students due to take GCSEs and A-level exams in 2021 should be prioritised for Covid-19 testing to reduce “ongoing disruption” to their learning.
Reports have suggested there could be a delay to the exam timetable next year to help deal with disruption caused by coronavirus – which kept some pupils out of school for months this year.
However, unions have suggested different changes are needed amid the fallout from the pandemic.
“Qualifications awarded on the basis of a series of exams, where students’ experiences of teaching and learning next year could be very different because of local lockdowns or other restrictions, will be unfair and may lead to additional disadvantage for some students compared to others,” Paul Whiteman from the NAHT said.
“The right approach to alleviate this issue is the adjustment to assessments and exams in 2021 to take account of the fact that students may not have covered the full course content.”
The NAHT’s general secretary added: “However, there is now a very short timeframe of opportunity to achieve this.”
Mr Barton from the ASCL told The Independent: “The benefit of shifting exams to a later date is really quite marginal compared to the scale of what has happened.”
The return to school last month was the first time all students were allowed back in the classroom since March.
Mr Barton told The Independent: “There has to be a robust contingency plan for those who are unable to sit exams or whose preparation over the next few months is very badly disrupted.”
“We are proposing some form of staged assessment in the autumn or spring term to provide a basis for awarded grades for students in these circumstances.”
He added: “But time is running out and the government needs to show a greater sense of urgency.”
Mr Williamson told the Education Select Committee there will be an announcement this month concerning the 2021 exams.
Days later, a government U-turn meant students could take their Centre Assessed Grades if higher than their moderated ones.
The Independent has approached the DfE for comment.
Additional reporting by Press Association