They fear the penalties will damage relations between schools and families.
In February, the Government gave schools powers to issue on-the-spot fines of up to pound;100 if children missed lessons without permission.
But not a single parent has reported receiving one of the penalty notices since the initiative was launched.
The lack of take-up has been blamed on each local authority having to consult police and schools and to set up a code of practice before fines can be issued.
Responses from 50 local authorities to a TES survey show that most councils are still undergoing this process and do not expect to have their plans in place until September.
Ten have decided they will not let heads issue fines. Others are expected to follow suit when they complete their consultation in the summer.
Wandsworth said it would use new-style parenting contracts but not the fines. Malcolm Grimston, Conservative councillor and cabinet member for education, said "There is a real feeling that the on-the-spot fines are just a gimmick."
The London borough of Newham and Thurrock council have also decided against using the fines.
Other authorities including Richmond-upon-Thames, Newcastle, Lincolnshire and Sandwell are planning to let education welfare officers, but not headteachers, issue the fines .
Steve Krawczyk, education welfare services manager for Lincolnshire, said:
"As the revenue generated by the scheme must come to the local authority, it would be unreasonable to expect the burden of issuing the penalties to fall to schools and the police."
Some local authority officials said they had been deterred by the bureaucracy involved.
A Department for Education and Skills spokesman dismissed the TES survey and said it was confident that all authorities would be using the penalty notices by the end of the year.
A TES poll on the fines earlier this year found that only one in 10 heads felt they were ever likely to use them.
Phil Willis, Liberal Democrat education spokesman, said the fines were a "barmy idea" which would drive a wedge between parents and schools.