Education Secretary Gavin Williamson has been told to "rethink his priorities" amid reports that traditional A-level grades could be overhauled.
Ministers are said to be considering changing A-Level marks to a numerical system similar to GCSEs to tackle concerns about grade inflation.
But Labour warned Mr Williamson against "playing around with the grading system" and urged him to focus on helping children catch up from the massive disruption caused by the pandemic.
Record numbers of pupils received top marks in their A-levels on Tuesday, with nearly 45% of students receiving an A or A*.
The Government insisted that this year's results are not comparable to previous years due to the pandemic.
And exams next year are expected to include some mitigations to help pupils after so much disruption.
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A-levels are currently graded A* to E, whereas GCSEs were changed to offer 9 to 1 marks to tackle grade inflation.
Officials are said to be considering a similar overhaul for A-levels but it is understood that ministers want to see the results of a consultation on plans for next summer's exams, which is due in the autumn.
A Government source told the Mirror: "It's highly likely that it's an idea which will be considered by ministers as soon as you sit down to have a conversation about grade inflation."
It is thought that a revamp of the grading system would not be ready to be imposed next summer - if the Government does decide to press ahead.
Shadow Education Secretary Kate Green told BBC Radio 4's Today programme: "I think that is just tweaking the system to get the Government out of a difficult story.
"We shouldn't be just playing around with the grading system here, we should be thinking about the quality of teaching and learning that children are receiving.
"It is not even crossing my radar at the moment. There are so many other greater priorities after a year in which children and young people have seen immense disruption to their education.
"I think Gavin Williamson needs to rethink his priorities and give the right support to children and young people."
NAHT boss Paul Whiteman said the idea was "unrealistic".
He said: "When GCSE grading changed, there were new specifications introduced and it took four years from the first teaching of those, to the point where all GCSE’s received numerical results.
"There is an opportunity here for government and Ofqual to review the current system’s reliance on terminal exams and grading by comparable outcomes. This requires meaningful consultation to ensure the fairest system for students.”
The bumper set of top A-level results also triggered concern about widening disparities between private school and state school pupils.
Some 70.1% of independent school students achieved A or above, compared to just 39.3% of comprehensive pupils.
Exams regulator Ofqual also pointed to how the pandemic had deepened inequalities for Black pupils, children receiving free school meals, and students from deprived backgrounds between 2019 and 2021.
Boris Johnson's former catch-up tsar warned over "growing inequality" in education could be a grim legacy of Covid-19.
Sir Kevan Collins, who quit his post in June, said: "There's a huge risk that one of the legacies of Covid, the education legacy of Covid, could be growing inequality.
"Now, to tackle that and to deal with that, we need a comprehensive and robust long-term plan.
"I don't believe the recovery will happen naturally and I think, if we don't do something tangible about it, we will have growing inequality in our education system."
It comes amid speculation that the PM could replace Mr Williamson with Equalities Minister Kemi Badenoch in a Cabinet reshuffle.
The Education Secretary has come under sustained criticism over his record during the pandemic.
