Teachers told researchers the tests, which were brought into some schools in September, distracted them from getting to know their pupils.
Many said the tests themselves were unreliable, duplicated work and did not marry with existing assessment systems.
Ministers say a fair baseline is needed to ensure pupils reach their potential.
The tests, which are being brought in to all schools from this September, measure basic reading ability, numeracy and writing, as well as children’s social and emotional development.
This is done in one-to-one assessments with teachers, who use checklists that include a series of questions such as whether a pupil can maintain concentration when listening to others or can subtract using single-digit numbers.