Schools in England will be able to appeal against A-level and GCSE grades free of charge, according to the education secretary.

Gavin Williamson said it would be a “shocking injustice” if cost stopped appeals being made on behalf of pupils with a “strong and legitimate” case.

His announcement came amid further criticism of the government’s handling of the exams system after thousands of pupils in England had their results downgraded.

Protesters gathered outside Downing Street on Friday chanting for Mr Williamson to be sacked, a call echoed by some opposition MPs.

But prime minister Boris Johnson insisted that he has confidence in Mr Williamson and described the system as “robust”.

Conservative MPs have voiced concerns about the process used by exam regulator Ofqual to moderate A-level results, with Sir Robert Syms suggesting the Westminster government may have to follow Scotland’s lead if the appeals procedure failed to deal with the issues.

The SNP-led administration at Holyrood opted to allow results estimated by teachers to be accepted.

Greater Manchester mayor Andy Burnham also said he is considering a legal challenge against Ofqual over the “unfair” A-level results process, given the impact on pupils in his region.

Outlining how the government did not want to deter schools from appealing, Mr Williamson told the Times: “I do not want a youngster to feel they are in a situation where there is a strong and legitimate case for grounds for appeal, but an appeal is not made on grounds of cost. That would be a real, shocking injustice.

“You will have obviously a large number of appeals. But I would rather have a strong, robust fair appeals process that makes sure that youngsters get the grades that they deserve as against being in a situation where there is an injustice that carries on.”

Mr Williamson again said there would be “no U-turn” on the grading system, claiming this would “severely erode” the value of qualifications and lead to grade inflation.

Robert Halfon, the Conservative chairman of the Commons Education Select Committee, earlier expressed concern that Ofqual’s model to moderate A-level results penalised disadvantaged students.

He called on the regulator to publish details of the algorithm it used to make its calculations. “I am worried about it because some figures suggest that disadvantaged students have been penalised again,” he told BBC Radio 4‘s The World At One.

“I am also worried about further education colleges, because they have been improving in recent years and yet they seem also to have suffered under this grading system.

“If the model has penalised disadvantaged groups, this is very serious and if it has disadvantaged colleges, that has to be looked at. Ofqual will have to adjust the grades.”

Ofqual has said that a “rare few centres” put in “implausibly high judgments”, and said that an appeals process is in place to correct any mistakes.

Shadow education secretary Kate Green warned there could be a “deluge” of appeals from students unhappy with their A-level results.

She said it may prove impossible to get them all processed in time for students to take up their university places.

Liberal Democrat education spokeswoman Layla Moran called for Mr Williamson to step down from his role with immediate effect.

She said: “Gavin Williamson is an education secretary out of his depth and out of excuses. He must take responsibility for his mistakes and step down with immediate effect.

“Our young people and our country cannot afford these blunders to continue into September, ahead of a potential second wave.”