They have found that the response can be effectively controlled by using ear acupuncture.
Some patients are so sensitive to dental equipment that they will gag uncontrollably as soon as an instrument touches their mouth. Others will start to gag at the mere thought of dental work.
This makes it impossible for dentists to carry out any kind of work at all.
100% success
The treatment involved inserting acupuncture needles into an anti-gagging point on each ear, followed by manipulation of the needles before dental treatment was started.
Participants in the study who had previously avoided dental treatment or who had only been able to receive treatment with sedation, were all able to withstand a trip to the dentist's chair.
They successfully received a range of treatments including fillings and tooth extractions and on all occasions were fit to leave the surgery and travel home unaccompanied.
However, the researchers have stressed that ear acupuncture should only be carried out by people properly trained in the technique.
Vagus nerve
It is thought that this form of acupuncture might work by causing the release of chemicals that influence the functioning of the vagus nerve that controls swallowing and gagging.
The researchers did not rule out the possibility that the patients simply relaxed because they thought the acupuncture would do them good.
But lead researcher Dr Janice Fiske, of the department of sedation and special care dentistry at Guy's Hospital, told BBC News Online: "You would not expect 100% success with just a placebo effect especially as the patients had had the problem for a long, long time and their attitude was it probably won't work."
Acupuncture has been successfully used to stop nausea and vomiting in chemotherapy patients and pregnant women.
The research is published in the British Dental Journal.