Doug McAvoy, the NUT general secretary, said: "It is clear that the provision of supply teachers made the tests and tasks more manageable, but availability was patchy. This situation needs urgent review and would be helped by an undertaking from the Government that it will meet the full cost of supply staff."
The London University Institute of Education carried out the research on key stages 1 and 2 at 800 schools while King's College, London, looked at KS3 in 400 schools. The NUT supplemented this work by analysing questionnaires from a further 2,870 schools.
Both the institute and the NUT found teachers' main concern was that half a term's teaching and learning was disrupted by the tests for seven-year-olds.
A total of 59 per cent of KS1 teachers in the institute's research and 49 per cent in the NUT survey said the whole school was disrupted, not just the children taking the tests. Curriculum planning was also upset, they said.
An NUT report said: "The majority of teachers said supply cover had made the tests more manageable. Headteachers, on the other hand, emphasised the difficulty of finding sufficient supply cover at the same time as it was being sought by all other primary schools.
"More than a third of teachers in the survey . . . pointed to an increased workload arising from the lack of supply provision. This was particularly the case in relation to marking, collating and reporting test results which 56 per cent said was carried out without supply support."
Support was also a problem during the tests for 11-year-olds. The institute found that most teachers could not have managed without it though the NUT found that 58 per cent of teachers in its survey prepared for and administered the tests without help.
At KS3, nearly all teachers in the King's College research said large numbers of able pupils had gone down one, two or even three levels compared to their teacher's assessment.