Steve Sinnott, general secretary of the National Union of Teachers, said that schools might have to set up special homework clubs or introduce extra lessons so pupils could complete their coursework under supervision. The NUT and the NASUWT said they would fight any moves by headteachers which allowed this to increase teachers' workload.
Mr Sinnott also said that he was saddened by the move. He said: "Coursework was introduced to increase the breadth in subjects and get pupils used to working on their own at home, preparing them for times when they will have responsibilities which cannot be dealt with just by working from nine until four."
The plan was revealed in a letter sent in March by Ken Boston, QCA chief executive, to Ruth Kelly, then Education Secretary, discussing proposals to revamp coursework which will be finalised in the autumn. He argued it would "improve authenticity and fairness" to increase the amount of coursework done in controlled conditions.
"We recognise that the practice of students carrying out coursework at home and the wide availability of the internet have created greater opportunities for malpractice," he said.
Allowing pupils to do more coursework in school could even reduce the burden on them, Dr Boston said, because "they would normally take less time to complete their task under controlled conditions than otherwise".
Mr Boston suggested scrapping GCSE maths coursework, but stressed he did not want to cut coursework for most subjects.
MPs on the Commons education select committee have announced they will hold an investigation into coursework cheating this autumn following reports in the Guardian this week by Barclay Littlewood, owner of ukessays.com, that he made pound;1.6 million a year, including pound;90,000 in one week in May, by selling essays for pound;400 each.
The DfES said that the QCA's recommendations were likely to be adopted. A spokesman said that, in future, coursework will "only be used where it is the most valid way of assessing subject-specific skills".