The charity, which is currently launching the second year of its Reduce the Risk campaign, estimates that half of all cancers are preventable.
While the most significant risk-reducing lifestyle change is stopping smoking, obesity is linked to an increased risk of bowel, kidney, oesophageal and stomach cancers, as well as womb and breast cancer in post-menopausal women. This means that staying in shape and eating and drinking healthily are extremely important.
But 50 percent of respondents in the survey carried out for Cancer Research UK by BMRB were overweight or obese (body mass index over 25 kg/m) - and 50 percent of those said they did not believe eating healthily could help reduce the risk of cancer.
Sixty-four percent did not know that regular exercise could reduce the risk, 65 percent were unaware of the importance of maintaining a healthy body weight, and nearly 80 percent said they did not recognize the importance of consuming alcohol only in moderation.
Also of concern is the 26 percent of obese and overweight people who said they would not actually like to lose weight.
"It's worrying to think that people are in denial about their weight," said Dr Lesley Walker, director of cancer information at Cancer Research UK. "These results show that far too many of those at greatest risk are choosing to ignore their weight. They are unaware of their increased risk of cancer and unaware of many of the benefits of losing weight."
A report published in The Lancet in November (vol 366, no 9499), estimated that 35 per cent of the 7 million deaths from cancer in 2001 were caused by a lifestyle that could have been changed, and drew attention to nine modifyable risk factors.
In this instance, the researchers from Harvard University based their findings on a comprehensive review of scientific studies and other sources such as government reports.
The Reduce the Risk campaign is a five-year initiative, which is targetting GPs' surgeries, health promotion units, hospitals and outpatient departments throughout the UK with leaflets and posters on its key messages.
Together with the charity Weight Concern, Cancer Research UK has come up with a set of weight management guidelines known as Ten Top Tips, which will form a major part of the campaigning effort in 2006.
The most recent figures from the UK's Department of Health indicate that 59 percent of women in England and 66 percent of men were overweight or obese in 2003.
Cancer is diagnosed in more than 270,000 people in the UK each year.