A senior Tory MP tonight suggested Gavin Williamson would be sacked in the next Cabinet reshuffle.
Former minister George Freeman said the Government's handling of the A-level and GCSE regrading was a "total shambles".
Asked if a minister should take responsibility for the fiasco, he said: "Ultimately, the Prime Minister is in charge. And I think he will want to take firm control of this and get a grip and show that his Government is taking the life chances of a generation of children seriously.
“I'm told the Prime Minister's planning to reshuffle in the autumn, and I dare say he wants to take everything into account."
Speaking on Times Radio, Mr Freeman said people were baffled as to how the Government got the exam problem so badly wrong after being given months to get ready.
"I think one of the reasons I called it such a shambles is that they had so long to prepare,” he said. “This was obviously going to be an issue back in March, it was clear to anyone with any experience of schools or children that there was going to be a problem: how are we going to handle the exams?
“I do accept that handling Covid has been an unprecedented emergency. And it's required the prime minister and other ministers to make extraordinary decisions and judgments with very little notice. And obviously, mistakes will be made.
“I'm not an armchair critic, but I just think this has been so obviously coming for months. I think many people will be scratching their heads and wondering how on earth this was allowed to happen."
It comes after Mr Williamson apologised following a major U-turn by the Government which will see tens of thousands of A-level students in England receive increased grades.
Following criticism from students and headteachers and complaints from dozens of Tory MPs, grades will now be based on teachers’ assessments rather than a controversial algorithm devised by regulator Ofqual.
Prime Minister Boris Johnson and Mr Williamson had previously defended the “robust” system, which saw almost 40 per cent of grades reduced from teachers’ predictions.
The change will also apply to GCSE results in England, which are due to be released on Thursday.
Mr Williamson apologised for the handling of the process, which followed the cancellation of exams due to coronavirus.
Ofqual’s chairman Roger Taylor admitted the regulator had gone down the “wrong road”.
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The algorithm was meant to moderate the process of awarding grades, preventing teachers awarding what the exams watchdog described as “implausibly high” marks to pupils.
But it came under fire over its perceived unfairness and the way it particularly appeared to penalise bright children from disadvantaged schools.
Mr Williamson accepted it had produced more “significant inconsistencies” than could be rectified through an appeals process.
Mr Williamson said: “This has been an extraordinarily difficult year for young people who were unable to take their exams.
“We worked with Ofqual to construct the fairest possible model, but it is clear that the process of allocating grades has resulted in more significant inconsistencies than can be resolved through an appeals process.
“We now believe it is better to offer young people and parents certainty by moving to teacher-assessed grades for both A and AS-level and GCSE results.
“I am sorry for the distress this has caused young people and their parents but hope this announcement will now provide the certainty and reassurance they deserve.”