The survey of more than 200 parents found that nearly three-quarters felt league tables were less important in choosing schools than other factors such as their curriculum, facilities, location and how they dealt with poor behaviour.
Just 31 per cent said they had used tables when picking their children's primary schools, while 39 per cent said the figures had helped them choose a secondary.
The poll, which was carried out for the GTC by Mori, also indicated that parents felt that league tables were one of the least helpful ways of finding out how their children were doing.
Only 27 per cent said league tables were very useful for this purpose. In contrast, verbal feedback was strongly appreciated by 79 per cent of respondents and written feedback by 71 per cent.
The GTC said that parents seemed generally less hostile towards league tables than teachers, but that their scepticism was still significant.
The council has been pressing the Government to scrap league tables and pupil assessment in their current forms.
Under its plans, schools would need to test only a representative sample of pupils in each year, rather than every child, and they would be allowed to use a bank of standard tests in-house rather than external exams.
The council will be holding meetings over the next three months with a range of parents' groups, including the National Confederation of Parent Teacher Associations, to help shape its proposals.
David Butler, the NCPTA's chief executive, said: "Parents want useful information about their childrens' schools and they see league tables as only one source of information.
"A more sophisticated and less competitive style of presenting this information would certainly help to make parents feel more informed."