Corrected test papers for all 11-year-olds and 14-year-olds have been returned to schools this week, but pupils may not know their official grades, known as "levels", until the beginning of next term.
Ministers are said to be furious about the delays which mean that many schools will be unable to include levels in end-of-term reports to parents.
Teachers are being sent mark sheets which enable them to convert the marks into levels - a job that is usually done centrally. But heads and some teachers' union leaders are advising their members not to carry out the conversion at a time in the school year when they are already under pressure. So pupils will be able to see their marks and percentages but will not know how they translate into levels.
The mix-up comes at a bad time for the Government, which has promised to cut down the amount of paperwork in schools.
The Qualifications and Curriculum Authority, which oversees the tests, says the calculation of the levels in papers in English, maths and science, will take only about one minute for each pupil. It is the first time the results have been processed by computer and the authority said yesterday that it could not say whether all schools would have their results by the end of term, the third week in July in most areas.
Dr Nick Tate, the authority's chief executive, has told schools in a letter: "The contractor appointed to process the results has experienced a number of technical problems leading to slippages in the planned schedule. We are naturally very sorry for any inconvenience this causes schools. We are doing all we can to keep the delay to a minimum."
David Hart, general secretary of the National Association of Head Teachers, which is advising its members not to ask teachers to carry out the conversions, said that the amount of work involved in secondary schools was quite substantial. He added: "It's a dog's dinner. This is the straw that breaks the camel's back over workload and bureaucracy."
Heads had the choice of hoping the results would arrive in time for this term's reports, sending out just teachers' assessments of pupils' levels, or waiting until next term.
Doug McAvoy, general secretary of the National Union of Teachers, accused the authority of trying to keep parents in the dark. He said news of the delay had been slipped out late on Tuesday.
"If this only involves a little bit of work, why doesn't Dr Tate find someone to do it? Primary schools are very busy at this time of year with activities such as sports days and outings."
The moderate Association of Teachers and Lecturers said it was dismayed that children would be kept waiting and schools would have great difficulty getting the grades out in time.
The Department for Education said it regretted the delay and was "taking a keen interest" in the matter.
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