The report by Becta, the educational technology agency, has emerged as the Health Protection Agency called for the Government to consider investigating how safe wi-fi is to pupils and teachers.
The TES has obtained an extract from the Becta study, which was carried out seven years ago when wireless systems were first being installed in schools, but it was never published.
The report said the radiation produced by any device involving wireless technology raised health and safety questions. "During the testing carried out by Becta, which involved using at least six sets of equipment simultaneously, some engineers complained of headaches at the end of the working day," it said. "But whether this is due to exposure to radio waves or some other factor is unclear."
The discovery of the report comes as campaigns grow against the use of wi-fi networks in schools. Several have discontinued their use after staff complained of adverse health effects.
Philip Parkin, the general secretary of the Professiona* Association of Teachers, has called for a full investigation into the networks.
"We continue to be concerned about the possible effects of wi-fi, particularly on children whose brains and bodies are still developing," he said.
But government scientists have said there is no credible research to back up health fears about suchnetworks, although no research has proved them to be safe either.
A Becta spokesman said it had not carried out any further investigation on the engineers' headaches and that it deferred to the Health Protection Agency on health and safety issues.
Dr Michael Clark, the HPA's science spokesman, said: "A problem with very common symptoms such as headaches is that they can be caused by many things."
Recent studies had confirmed that typical exposures to radio waves from wireless networks were extremely low, Dr Clark said.
"The levels are also lower than those from mobile phones, FM radio, television and the numerous other radio signals in the classroom."
But he said manufacturers and the Department for Education and Skills should consider commissioning an independent study of wi-fi signals in schools.
Mary Barker, the general secretary of the ICT teachers' association Naace, said wi-fi was a "wonderful facility" that allowed for more flexible lessons, but that research was needed so teachers could be confident about its safety.