This compares to 70 per cent who were aware of the link with heart disease.
The charity is aiming to raise consumer awareness of the benefits of losing weight with its Race for Life, an organised run or walk taking place across the UK between May and July.
However the findings also present an opportunity for the food industry to communicate the benefits of weight loss.
Professor Jane Wardle, director of Cancer Research UK's Health Behaviour Unit, said: "Excess body fat is not harmless 'extra padding', but active tissue producing hormones that can increase the risk of cancer. In order to lose weight and then maintain a healthy body weight you need to eat less and be more active. Even small weight losses have been shown to have a beneficial effect on health."
Dr Lesley Walker, director of Cancer Information at Cancer Research UK, added: "The results of this survey are extremely worrying especially as being overweight is the major preventable risk factor for cancer in non-smokers."
"Post-menopausal women who are overweight have a greater risk of developing breast cancer and there is also evidence of a link between being seriously overweight and cancer of the womb, kidney, bowel and oesophagus."