"Chemotherapy drugs kill rapidly growing cells such as cancers, but they also attack healthy parts of the body.
Doctors at Southampton General Hospital believe targeting just one organ can prevent side effects.
They also say it means they can give higher doses without causing damage to the patient.
Chemotherapy drugs are normally injected into the veins of patients. However, the whole body, rather than just the tumour, is exposed. It results in side effects such as fatigue, feeling sick, hair loss and damage to fertility.
Two patients in the UK have now received chemotherapy focused on just their liver. Both had a rare eye cancer which had spread to the liver.
The operation works by inflating balloons inside blood vessels on either side of the liver to isolate it from the rest of the body.
The liver is then pumped full of chemotherapy drugs, which are filtered out before the liver is reconnected to the main blood supply.
It means only a tiny fraction of the chemotherapy dose ends up in the body.
Dr Brian Stedman, a consultant interventional radiologist, said: “To cut off an organ from the body for 60 minutes, soak it in a high dose of drug and then filter the blood almost completely clean before returning is truly groundbreaking.
"Previously, the outlook for patients specifically suffering from cancer which has spread to the liver has been poor because standard chemotherapy’s effect is limited by the unwanted damage the drug causes to the rest of the body."
The surgery took place in the past three months and both patients are said to be doing well and their tumours “all look smaller”, he said.
Dr Stedman told the BBC: “In 20 years’ time the idea of injecting a drug which poisons the whole body for a cancer in just one small area will seem bonkers.”
He suggested that any organ which could be easily separated from the blood supply, such as the kidney, pancreas and lungs, would be suitable for this kind of approach.
However, he said the method was “in its infancy” and he was “not sure this is the finished product or the end of the story”.
The technique is also being tested in the US and elsewhere in Europe.”