The Public and Commercial Services Union has written to the Commons education select committee asking it to look into the way the QCA is handling the privatisation of its maths test-development section.
It says the QCA has broken Cabinet Office guidelines by seeking private-sector applications for the contract to develop national curriculum tests without investigating the advantages and disadvantages of public-sector options.
Around 40 QCA staff could transfer to the private operator when the contract, worth around pound;1.5 million a year, is signed. The privatisation comes because the QCA has been advised to separate its test-development and administration functions and its work regulating the testing system.
The union says the QCA was asked to carry out the public sector comparison but refused.
Dean Rogers, its national officer for London and the South-east, said: "If you are effectively giving public money to someone to spend for you, there is a requirement to test whether they are going to be spending it more efficiently. The QCA is showing a blatant disregard for accountability and due process."
A QCA spokesman said: "We do not believe that the public sector comparator is applicable in this case. However, we will continue to discuss the issue with the union."
Barry Sheerman, chairman of the select committee, said that he would seeking answers on the issue when senior QCA officials come before it next month.