Only a small majority - 55 per cent - of 9,000 staff responding to a poll by the National Union of Teachers said they would refuse to administer key stage 3 tests.
This represents just 4,921 of the union's 72,000 secondary members. The NUT has now rejected the possibility of any boycott of the tests.
Last autumn, the union had to call off a boycott of ks1 and ks2 tests after only a third of papers were returned.
Support from half of primary members was needed for action to go ahead.