Exam boards are under mounting pressure to make appeals free so that the poorest children do not miss out.
Schools usually have to pay between £8 and £70 per query for GCSE and A-level re-markings.
But exam boards are being urged to follow the lead of their Scottish counterparts, and waive fees this year to avoid putting students from deprived communities at a disadvantage.
Leora Cruddas, chief executive of the Confederation of School Trusts which represents academies, said that charging a fee to appeal exam results may "put schools off appealing". She warned that with education budgets strained by extra coronavirus-related costs, charging risks "unfairly disenfranchising" certain schools.
Appeal fees may also create "perverse incentives" where head teachers are put off appealing grades because they want to save money, she added.
Teenagers in England will this month receive A-level and GCSE grades calculated using the statistical model after all exams were cancelled due to coronavirus. The model takes into account factors including pupils' past performances and the last three years of schools' grades in the same subjects.
Geoff Barton, general secretary of the Association of School and College Leaders, said that fees must be waived to ensure a "level playing field" and that "the ability to appeal would not be constrained by the funding that is available".
Robert Halfon, Tory chairman of the education select committee, also called for appeals to be free. "Otherwise, the system will favour the well-off, the well-heeled and sharp-elbowed. It will basically favour schools with big budgets and surpluses rather than those who would rather spend money on tuition and making sure pupils catch up."
Last month, the committee said that less affluent schoolchildren risk not getting the results they deserve as a result of an "unfair" appeals system. MPs said the process for allowing students to appeal, set out by England's exams regulator Ofqual, is too complicated and could favour children with wealthy parents.
Layla Moran, education spokesman for the Liberal Democrats, said that pupils should be allowed to appeal their grades directly with the regulator without fees. "The Government must confirm that pupils will be able to appeal grades free of charge," she said.
Last year, a "clerical check" to ensure all pages were marked and all marks added up correctly was the least expensive, costing £8.05 for GCSEs and £16.10 for A-levels with AQA. A "priority review of marking" cost up to £46.40 with Edexcel for GCSEs and rising to £55.90 for A-levels. For AQA, it was £37.55 for GCSE and £51.75 for A-levels. OCR charge £59.80 for a "review of marking" for A-levels, rising to £71.95 if one wants to see a script.
Most boards waive fees if the grade is changed as a result of the re-mark.
Earlier this week, the exam watchdog announced that pupils will be allowed to challenge "unfair" A-level and GCSE grades after the exam regulator changed its stance in the face of a backlash from head teachers. Schools can now appeal results in "exceptional" cases if they believe students are incorrectly marked down by the statistical modelling used to calculate the grades.
It came in the wake of the Scottish results fiasco, where close to 125,000 predicted grades were downgraded by the Scottish Qualifications Authority.
The Joint Council for Qualifications, an umbrella group that represents the country's leading exam boards, said that no decision has yet made so far on whether school will be charged fees this year for appeals.
Ofqual said it has no powers to require exam boards to waive fees for appeals, but added that complaints about bias or malpractice are not appeals, and should be investigated without fees.
"The arrangements in place this summer are the fairest possible to enable the majority to move on to further study or employment as planned," a spokesman said.
"Overall, students will get the best estimate that can be made of the grade they would have achieved if exams had gone ahead.
"But it is right that their school or college can appeal if they believe there has been an error or that the moderation process has not produced a reliable result."