The climbdown came as Downing Street effectively conceded this year’s results were unfair, just days after Boris Johnson described them as “robust”.
He had faced growing pressure to act as two government ministers broke ranks to express their concerns about the controversial new results system, introduced after the coronavirus pandemic cancelled exams.
Within hours Mr Williamson announced that an algorithm, which had downgraded four in 10 teacher assessed marks, had been ditched.
Instead A-level and GCSE students in England will receive the original grades decided by their teachers, following similar U-turns in Wales and Scotland.
No pupils will lose out, however, as those who had their results marked up instead of down will be allowed to keep the higher grade.
Ministers will also remove a cap on the number of university places this year, in a bid to ensure as many pupils as possible are able to find a place on their preferred course.
Last night Cambridge said it would “be in touch” with all those who held an offer at the university.
But the Russell Group of leading universities called for urgent clarification from ministers on extra financial support for institutions now facing a potentially dramatic rise in student numbers.
And University College London (UCL) announced that students who had now met its offer to study medicine would be guaranteed only a deferred place on next year’s course.
As he made the announcement, Mr Williamson said: “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.”
His apology was echoed by Roger Taylor, the chair of Ofqual, the exams regulator, who said: “I would like to say sorry.”
Last week Mr Williamson defended the algorithm and insisted there would be “no U-turns”.
He warned that to follow Scotland’s lead and dump the new system, designed to standardise marks, would deliver “rampant grade inflation”.
But after the change of heart he said it had become apparent over the weekend that there were too many outliers in the amended results.
Ministers hope the U-turn will draw a line under the row, but a new YouGov poll found 40 per cent of the public believe Mr Williamson should resign, compared to just 21 per cent who think he should stay in post.
Mr Williamson shrugged off the polls results last night, saying what the public really wanted was “action” on exams.
Sir Keir Starmer, the Labour leader, described the U-turn as “screeching” and criticised ministers who, he said, had had months to prevent the crisis.
Earlier Boris Johnson had broken off from his holiday in a bid to try to head off the brewing crisis.
He held a meeting with Mr Williamson and senior government officials, dialling in from the start of his week-long break in Scotland.
Downing Street also appeared to concede the algorithm had produced results which were unfair.
The prime minister’s official spokesman said the government continued to work “to come up with the fairest system possible”.
But he added that the prime minister still had confidence in Mr Williamson.
As pressure from backbench Tory MPs grew, paymaster general and cabinet office minister Penny Mordaunt said she was “seeking a further meeting” with the Department for Education after speaking with students and parents about exam results.
“This group of young people has lost out on so much already, we must ensure that bright, capable students can progress on their next step,” she said.
Sir Iain Duncan Smith, the former Conservative leader, also called for the controversial algorithm to be dropped.
“No algorithm is going to sort our problem out,” he told LBC Radio.
The Independent reported last week that pupils were prepared to take to the streets in protest at widespread downgrades.
Since then ministers have endured days of public protests as students railed against what they said were grade changes that disproportionately affected poorer pupils.
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