If they do not, says a letter to governors from the Department for Education and Employment, the schools face a "missing" entry in the forthcoming league tables.
The department already has the test results, which were automatically passed to the computer agency drawing up the league tables by the external marking agencies. But it needs the schools' co-operation to get teacher assessments.
Penny Bassey, headteacher of St Andrew's C of E Primary School in Skegby, Nottinghamshire, has written to The TES (see Letters, page 22) complaining about this "bullying" by the department.
The school decided last summer not to submit the results to the DFEE because it considered league tables "contrary to the Christian ethos of this school", she writes. Yet that decision had been subverted by the external marking agency (in this case the Midlands Examinations Group), who passed the test results on.
"We are now," continues Mrs Bassey, "being arm-twisted into submitting our teacher assessments under the threat of 'missing' being put in the league tables. Since we consider our teacher assessments to be more reliable than the tests, we shall need to yield to this intimidation, notwithstanding the injunction of our school pastoral policy that 'bullying is not tolerated at St Andrew's School'."
It is not known quite how many of the country's 20,000 primary schools refused to send in their results. The National Association of Head Teachers, which appealed to governing bodies to block the results' publication, estimates that some 25-30 per cent may have done so.
"The regulations still say that it's the governing body's responsibility to pass on the results to the DFEE," said a spokeswoman for the NAHT. "Yet they get them automatically from the external marking agency. Governing bodies who passed a resolution not to submit them feel they've been robbed.
"It's a question of who owns the data," she continued. "And nobody seems to know."
Performance tables based on the 1996 GCSE, A-level and GNVQ examination results are due to be published by the Department for Education and Employment next week. The results, in full, plus extensive analysis, will appear in next week's TES.