Pressure is mounting on the Government over its handling of the exams system after thousands of pupils in England had their results downgraded.
It comes as protesters gathered outside Downing Street on Friday chanting for Education Secretary Gavin Williamson to be sacked.
Prime Minister Boris Johnson has insisted that he has confidence in Mr Williamson and described the system as "robust".
On Friday, Robert Halfon, the Conservative chairman of the Commons Education Committee, expressed concern that the model used by Ofqual 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.
Mr Halfon added that the appeals system needed to be broadened so that every student who felt they had lost out could use it.
"We have to have a wider appeals system, a quick appeals system that is for everyone, not just the sharp-elbowed and well-heeled," he said.
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.
Ms Green told The World At One: "I am concerned that if we have a deluge of appeals, which I think is quite likely given the fiasco we have seen over the last day-and-a-half, there just won't be time for students to have those appeals processed and completed, and universities will fill up those places."
She added: "As a one-off measure this year, we have to do something for these young people, otherwise we are writing them off for the whole of their life chances.
"I think it is right that this year we take exceptional measures, give those young people every possible opportunity to progress with their lives and make use of teacher assessments where we can't be confident that the algorithm and the Government's model has delivered fairness to very, very large numbers of students."
Liberal Democrat education spokeswoman Layla Moran called for Mr Williamson to step down from his role with immediate effect.
"The shambolic handling of A-level results has left many young people in crisis," she said.
"Despite the warning signs from Scotland, the Education Secretary pushed ahead with plans which ignored teachers' advice and have disproportionately affected pupils from disadvantaged backgrounds.
"With this unfair system, he has created untold confusion and distress.
"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."
SNP MP Pete Wishart also added his party's voice to calls for Mr Williamson to step down, tabling an Early Day Motion (EDM) to Parliament.
He tweeted: "I am going to write to the Speaker to see if Parliament can be recalled.
"We need to hear from the Education Secretary on the exam crisis in England and to offer the opportunity to my English colleagues (and to Scottish Conservative MPs) to seek his resignation."