In Cambridge, St Laurence RC primary has refused to submit its results to the Department for Education and Employment.
The Government has threatened disciplinary action against both schools - the only ones which will not appear in next week's primary league tables.
Their heads have been warned they have a legal duty to supply the results and their local education authorities will be expected take action if they do not comply in future.
A DFEE spokesman said the ultimate sanction could be sacking the head, though only the governors have the powers to do this.
In April the Rosslyn school came under the aegis of Nottingham City council which has threatened to get tough with the school.
The governing body has agreed to meet Paul Roberts, the council's education director, next week, when he will try to persuade them to drop their opposition. Don Scott, a governor and the city's education chair will also urge them to do the tests.
Nottingham county, under the robust leadership of Fred Ridell became a test-free zone in the heyday of the dispute between the teaching unions and the Conservative government. But following Sir Ron Dearing's national curriculum review, schools have been taking the tests.
Ralph Surman, national executive member of the Association of Teachers and Lecturers, said the city's position at the bottom of the primary league tables could be connected to the fact that Nottingham schools put less emphasis on the tests. But he said he understood the school's defiance.
He said: "The situation is getting ludicrous. Teachers are teaching to the test and in some cases are getting children to learn by heart long phrases and lists of long words to help them do well.
"Schools are doing large amounts of revision work in the weeks before the tests. Nottingham has not taken the tests seriously in the past and this could be reflected in the results."
The governing body at Rosslyn does not rate the national curriculum tests and sets it own which teachers believe are more rigorous. The school received a good inspection report. Rosslyn's head, Charles Hurt, was in Spain this week and not available for comment.
A Cambridgeshire County Council spokesman said: "We made it clear that we expected the results to be supplied and now have a written assurance from St Laurence that it will do next year."
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