Two thirds of the 4,000 people questioned were unaware that being overweight or obese increases the risk of some cancers. And almost exactly the same number (67 per cent) did not know that a diet low in fruit and vegetables could increase their chance of getting the disease.
Scientific research has shown that at least half of all cases of cancer could be prevented but the new report suggests that this message has not reached many members of the public.
Cancer is diagnosed in more than 270,000 people in Britain each year.
The report also showed serious levels of confusion. Only one third of those surveyed mentioned drinking less alcohol as a way of reducing risk. But almost a quarter (24 per cent) believed living near power lines was a risk and more than one third thought stress was linked to cancer despite.
There is however no strong scientific evidence to support either of these beliefs.
But the charity said it was heartening that more than 90 per cent of those questioned knew that smoking increased the chance of developing cancer and the vast majority of people are aware that sunburn increases skin cancer risk.
A new five-year campaign will try to tackle other lifestyle changes such as healthy eating that are known to bring down cancer risk. Diet influences risk of stomach and bowel cancer and is likely to be important for cancer of the lung, according to Cancer Research UK. It may also affect our risk of breast, prostate, bladder, mouth and throat cancers.
"We estimate that half of cancer cases could be prevented. There is no magic pill to prevent us getting the disease but there are many things we can all do in our daily lives to improve our chances of avoiding it," said Cancer Research UK's chief executive Professor Alex Markham.
"Already we are making headway on tobacco. But our survey has shown there is a great deal more to do. Lack of awareness among the public is a major concern. It is important for people to realise that being a healthy weight and eating a properly balanced diet with plenty of fruit and vegetables can really make a difference to their cancer risk."