Their views were canvassed by the University of East Anglia and the National Children's Bureau for an evaluation of the Government's pound;700 million scheme to integrate children's services.
Plans for extended schools, published in July, stated that by 2010 all schools must provide "swift and easy referral to a wide range of specialist support services" and that some "may be delivered on school sites".
Extended schools are the Government's way of bringing schools into the Every Child Matters programme, although they are exempt from the legal "duty to co-operate" which other services must abide by under the Children Act 2004. Instead, they are expected to provide extended services, including childcare, parental support, community facilities and referral to specialists.
But parents said they would not want to be seen going to social workers on a school site and were concerned that records would not be secure.
The official evaluation of children's trusts - the umbrella organisations being set up by local authorities to bring together social services, health and education - has found that schools were likely to be on the margins of the move to integrated working.
The evaluation, funded by the Department for Education and Skills, found a huge culture clash between education and social services.
It found that headteachers were often frustrated by difficulties in contacting social workers and thought social workers focused on safeguarding children rather than preventative work.
Social workers believed that teachers had too narrow a focus on children's attainment.
Researchers said it was "striking" to find near universal support for the changes to children's services among those who work in them, but said there was a lack of clarity about the new roles and responsibilities.
The report said: "The vast majority (of headteachers) have no plans to become involved (with their trust)...This indicates that in England a very low number of schools are likely to be involved in the integration of children's services."
A separate study of the extension of full services to schools has found considerable anecdotal evidence that where a full range of services is provided on one site, they were improving standards and relations with families, although no hard evidence was available yet.
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