Instead of offering protection against potential health risks, two such devices acted as aerials and tripled the amount of radiation channelled into users, said watchdog the Consumers Association.
But Carphone Warehouse, whose hands-free sets were tested, disputes the latest findings, saying they are contrary to its own research.
Mobile phones have previously been linked to illnesses, including brain tumours, although scientific opinion is divided.
Managing director of Carphone Warehouse Charles Dunstone said: "We are surprised by the Which? report, as are several of
the industry bodies that we have been speaking to, as all other
research has contradicted their findings."
And Carphone Warehouse's Jonathan Hook told the BBC: "There is no specific evidence to support claims that mobile phones are damaging to health."
Thousands of UK customers have bought hands-free sets and shields in a bid to minimise the risks.
Amid increasing confusion over the risks of mobile phone use, Which? - the CA's trading arm - has sent its test results to the Department of Health-commissioned inquiry into mobile phone safety.
The Federation of the Electronics Industry said it was surprised by the results.
A spokesman said: "Tests made by FEI members and also at an independent laboratory have, without exception, shown that the absorption levels produced when using a headset are significantly less than those produced without a headset.
"All mobile phones on the market meet all relevant safety standards and recommendations with or without an approved headset."
'Shields offer little protection'
Which? tested two hands-free sets from Carphone Warehouse and BT Cellnet and found they channelled three times as much radiation from the phones into users' heads.
"The two models we tested triple the radiation to your brain, though we still don't know for certain whether that radiation is harmful."
Which? also tested phone shields and attachments that claimed to block radiation, but tests revealed they offered limited, if any, protection.
Mr Jacobs added: "As for phone shields, the ones we looked at don't help, so if you're thinking of buying one, don't waste your money."
The Department of Health said it expected a report in a few weeks' time from a panel of experts tasked to investigate mobile phone safety.
Dr Michael Clark, of the National Radiological Protection Board, said there was confusion about the type of radiation given off by mobile phones.
Dr Clark told the BBC: "What I am against is the scaremongering that goes on by the use of the term 'radiation' associated with mobile phones.
"They are radio-wave transmitters, they are not x-ray transmitters. It is not highly dangerous radiation."