Other schools said they would not have taken part in the trial if they had realised how much work was involved in the tests, which pupils take when their teachers think they are ready.
The tests are a centrepiece of the 10-year Children's Plan unveiled by the Government this week. The plan also includes proposals to make all new teachers gain a master's-level qualification and to remove more "incompetent" members of the profession.
The Government announced in June that the "single level" tests for key stage 2 and 3 pupils, which are expected to replace the present national tests, would be tried out in 484 primary and secondary schools in 10 local authority areas.
However, 73 schools have either dropped out of the trial completely or decided against entering children for the first round of tests last week.
A Qualifications and Curriculum Authority spokesman insisted the 15 per cent drop-out rate was relatively low. Schools that took part were mostly positive about the tests' impact on pupils, saying that the children had enjoyed them.
But several told The TES that they had withdrawn because of the work involved for teachers.
The trial relies on teacher assessment: staff are expected to judge pupils' abilities before entering them for the test. Schools said this had been the most labour-intensive aspect with teachers spending time filling in assessment forms, nervous about getting the level wrong.
Melanie Vine, head of White Court Primary School in Great Notley, Essex, said her school had pulled out because it was not able to give the trial the time it needed. "From the schools I have talked to, it is an awful lot of work," she said.
Nola Van Dam, head of St Thomas More Catholic Primary in Bexley, Kent, said if she had known how much work it involved before, she would have dropped out.
The Government is understood to be concerned that the trials could accentuate "teaching to the test".
Mary Bousted, general secretary of the Association of Teachers and Lecturers, said: "The danger is that it will quadruple the workload of teachers and mean pupils will sit multiple tests to find their level."
A spokesman for the Department for Children, Schools and Families said the response to the tests had been "overwhelmingly positive". He was confident the workload would decrease once all systems were in place.
Children's Plan, pages 16-20
Target culture is pushing teachers into making sweeping judgments of pupils based on their race and class, a report published today will warn.
It is in the latest research from the Primary Review. The report says the emphasis on hitting targets is affecting the way teachers see pupils and parents, as they can judge them according to how well their race, gender or class perform in tests.
Full reports, pages 12-13.