More than 1,600 people have signed a petition calling on Bath and North East Somerset Council to halt the rollout of 5G.
They claim the technology is untested and unnecessary, and could harm public health.
Despite getting enough signatures to trigger a debate by the council, leader Dine Romero said it was national government that needed to be persuaded.
Fiona Williams, who started the petition, told the full council meeting on July 23: “Nobody has been consulted about this rollout and no risk assessments have been carried out.
“There will be differences of opinion about 5G’s health effects, but what is clear is that there has been no safety testing, therefore there is no certainty that this technology is safe.
“This is all part of a wider agenda to use AI and robotics which ultimately threaten a core aspect of our humanity, the right to freedom and to privacy.
“With thousands of peer-reviewed studies pointing to biological harm from 4G wi-fi as well as 5G, with electrically sensitive people experiencing real physical effects, we’re asking you to adopt a precautionary approach and do the right thing by your constituents.”
5G technology is billed as offering faster mobile broadband connections with good quality connections.
Telecoms company EE insists it is safe, is very similar to 2G, 3G and 4G, the previous generations of mobile broadband, and will be rolled out under strict guidelines.
Studies from the World Health Organisation, Public Health England and the UK Health Protection Agency have all shown that 5G is not harmful to health.
But Ms Williams’ petition said there were health risks to children, pregnant women and the elderly or those with chronic illness, and could harm wildlife including birds and bees.
Vanessa Williams Grey, another public speaker at the meeting, said: “We’re in the midst of a global pandemic and as a local mother I believe that unless we act swiftly the negative impacts of 5G technology will trigger a similar health crisis.
“The council has a duty of care to all of its citizens and liability for public health but surely above all a responsibility to its most vulnerable, including future generations.”
She said the radiation could cause cancer, sleep disorders, cognitive impairment, dementia and infertility.
Paul McLachlan, who said electrical hypersensitivity causes him anxiety and poor sleep, said: “What is all this radiation actually doing to all of us?
“After Bath announced that 5G will be introduced in the city I want to make the council aware of the pain this will cause so many people. It affects us all in the long term, our children especially.
“As a family living in Bath, we do not consent to this rollout.”
Councillor Romero said the council would not debate the issue as members would only be able to give their opinions.
She suggested that the opponents of 5G wrote to their MPs and the Prime Minister as it Government that needs to be persuaded to halt the rollout.
Cabinet members will respond to the specific points made in the petition.
Stephen Sumner, Local Democracy Reporter
