The unions, which represent heads and classroom teachers, are canvassing the views of their members about further action over the tests, which are due to take place in June.
English teachers and the National Union of Teachers are already conducting surveys of support for a boycott.
The six unions said there had been no national pilot trial for the English tests as there had in maths and science. Teachers had been unable to plan because the tests had been introduced so hurriedly, the Government's advisers on exams had kept changing their minds and the tests conflicted with good teaching practice.
Ministers, who appear to have been surprised by the intensity of opposition, say the tests have been trialled over three years, more than any other exam.
Opinion among teachers about action against the tests is divided. Doug McAvoy, general secretary of the NUT, said: 'This will encourage our members to support the ballot on a possible boycott of the tests. I hope it will also mean that the other organisations will join us in such a boycott.'
The Professional Association of Teachers, which opposes industrial action, said it could not take part in a boycott. 'Nor can we encourage teachers to risk putting themselves in breach of contract, which is what those teachers who boycott the tests may well discover that they have done,' a spokesman said.
Heads of more than 600 schools have already said in reply to a questionnaire from the London Association for the Teaching of English that they would support a boycott.
The Department for Education said yesterday that school boycotts, even if they had the backing of governing bodies, would be illegal. Many governing bodies may balk at the idea of breaking the law.