Six hundred claims of misconduct by teachers and pupils in the key stage 1, 2 and 3 tests were reported to the National Assessment Agency last year, compared to 147 in 2000.
Teacher unions said it showed the pressure on schools to do better in tests was now intolerable.
Growing concern about cheating by teachers and pupils has also spread to GCSEs and A-levels. The TES has learned that coursework may disappear from most GCSEs and A-levels partly because of staff breaking the rules.
England's exams regulator is looking into claims that teachers are now under so much pressure to raise results that many virtually write coursework for pupils. Many staff admit this is so.
The Qualifications and Curriculum Authority accepts that coursework in most subjects cannot easily exist in a system which holds teachers accountable for their results by performance management and league tables.
Discussions at the QCA suggest that all GCSEs and A-level coursework will be scrapped within four years except in subjects such as art, music and design and technology, where there is an overwhelming case for its inclusion.
As GCSEs and A-levels began this week, a TES poll showed that GCSE coursework continues to be popular with parents. More than three-quarters of the 500 parents surveyed by FDS International said coursework should continue to be part of GCSE assessment, with only one in six believing it should be scrapped. Half of parents of Year 11 pupils in the poll confessed to helping with their children's coursework.
On the TES website this month teachers have owned up to illegally extending deadlines, overlooking plagiarism and writing work for pupils.
Many teachers have suggested the pressure to improve results, which leads them to allow multiple redrafts of pupils' work, makes in-course assessment a farce.
One said: "I'm busy marking GCSE coursework at the moment. I know full well that vast amounts of it is cut-and-paste but I'm going to pretend I haven't noticed."
Another said: "The cheating is absurd. We largely write and grade our own work."
Another said: "As an ICT teacher I cannot defend the now-accepted-as-the-norm practice of doing the coursework for the pupils.
My head of department reads answers to (the pupils) in lessons."