However by "fishing out" those immune cells and multiplying them in the lab, it should be possible to wipe out cancer, even when it has spread throughout the body.
"The body's immune system acts as the police trying to tackle cancer, the criminals," said Dr Sergio Quezada, the head of UCL's Cancer Insitute.
"Genetically diverse tumours are like a gang of hoodlums involved in different crimes - from robbery to smuggling. And the immune system struggles to keep on top of the cancer - just as it's difficult for police when there's so much going on.
"Our research shows that instead of aimlessly chasing crimes in different neighbourhoods, we can give the police the information they need to get to the kingpin at the root of all organised crime - or the weak spot in a patient's tumour - to wipe out the problem for good."
It means that, in future, doctors could look at the genetic profile of a tumour to locate the "flags" then engineer billions of special immune cells that could be transferred back into the body in large numbers to kill tumours.
Importantly, it would work on cancer that had spread throughout the body, because the underlying tumours would all have the same genetic "flag".
Researchers are hoping that the first trials will be carried out on patients within two years.
Prof Charles Swanton, from the UCL Cancer Institute, said the new approach could improve survival significantly, adding: "It gives us as an Achilles' heel to go for."
The research is published in the journal Science.