Some 63,380 GCSE results were challenged in 2006, up 26 per cent on 2005.
And 14,305 grades were changed as a result, a 22 per cent rise.
At A-level, requests for re-marks rose only 3 per cent to 53,336, with 5,778 grades changing as a result, a 2 per cent increase.
Nearly 16 million GCSEs and A-levels papers were marked.
Some 4,757 candidates were penalised for exam malpractice, a 5 per cent rise on 2005. The most common offence was bringing a mobile phone into the exam hall.
Overall, 775 young people were disqualified because of rule-breaking, with 463 punished for disruptive behaviour during an exam.
Mick Brookes, National Association of Head Teachers general secretary, said: "The whole system has to be reviewed. A monster has been created no one can control. In a system this size, there will be errors."
The Qualifications and Curriculum Authority, which published the figures, said the re-marks represented 1 per cent of the total number of entries.
The boards hit most targets for processing re-marks and appeals on time.
The authority also issued a warning after 78,833 pupils were approved to receive special treatment in exams, from extra time to the use of a bilingual dictionary and "supervised rest breaks" if, for example, they were dyslexic.
The regulator said it would carry out inspections to check the rules were not being flouted.
The number of pupils disqualified or losing marks from national tests also rose last year, from 79 to 626. Alleged cheating instances dropped from 600 to 579.