But one of Britain's leaders in the transplant field has disclosed that the advice is being ignored and says doctors must be prepared to take more organs from this source.
Professor Peter Friend, president of the British Transplantation Society, has warned that doctors must calculate the possible dangers against the real benefits.
"If we had plenty of organs and we just had to wait until tomorrow for the best one to turn up then that would be fine, we could say 'no risk please'," Times Online quoted Friend, also director of transplantation at Oxford Radcliffe Hospitals NHS Trust, as saying.
"I suspect there are a lot of potential donors with a history of cancer, perhaps in the distant past, who have been turned down. We need to say, 'What is the reason to discount these people?'" she added.
According to figures from UK Transplant, the transplantation agency, in the past two years, 195 organs have been taken from 67 donors who died of cancer, or who suffered from the disease earlier in their lives.
Seventeen of those donors died from brain tumours.
There is a record 8,000 patients awaiting a transplant, of whom about 400 a year die.