Sources at the education and skills select committee said its decision to cancel the investigation and another on creativity in schools was unavoidable as the body will cease to exist next week.
When the House of Commons returns in the autumn, new committees will be set up to scrutinise the separate departments of Children, Schools and Families and Innovation, Universities and Skills.
The TES has been told there is a good chance the inquiries will be picked up by the new committee.
However, some in the education world were shocked by the decision. Many organisations submitted written evidence after it opened in March, though it had yet to hear any oral testimony.
It won front-page headlines last month after England's General Teaching Council called for all national testing to be scrapped. The inquiry was widely seen as putting further pressure on ministers over school assessment and accountability.
Professor Margaret Brown, of the Advisory Council on Mathematics Education, which submitted evidence, said: "There will be an outcry if this does not go ahead."
Michael Reiss, director of education at the Royal Society, which also submitted evidence criticising the testing regime, said: "There is no more important issue in education at present than improving our assessment system. Whether a select committee looks at this or some other body, someone needs to."
The TES understands the decision to reorganise the education departments came as a surprise to the education and skills select committee.
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