Test results for 11-year-olds jumped from 48 per cent reaching the expected level in English in 1995 to 75 per cent in 2000, with similar rises in maths.
But the Statistics Commission said these improvements were largely down to teachers drilling pupils to do well in the tests.
There had been some rise in standards but the test results exaggerated the progress, the report said. "Ministers, and others who may want to use the test scores in a policy context, need to be made fully aware of any caveats about their interpretation."
The commission delivered its judgement after receiving a letter from Professor Peter Tymms, an academic at Durham university, who had studied the results. It did not back his conclusion that the tests should be dropped, saying there was "no real alternative" to using test scores for setting government targets for improving overall standards.