Health experts from World Cancer Research Fund, who conducted the poll, have described the figures as "alarming", given that 62% of the English adult population is currently overweight or obese.
Being overweight is known to increase the risk of developing 10 different cancers including bowel cancer, breast cancer (postmenopausal) and pancreatic cancer.
The poll also found that over half of Britons (54%) are not aware that physical inactivity can increase the risk of cancer and that around two fifths are not aware of the increased cancer risks linked to eating a poor diet (40%) or drinking alcohol (43%).
According to World Cancer Research Fund, after not smoking, being a healthy weight is the most important thing people can do to reduce their cancer risk.
It estimates that about a third of the most common cancers could be prevented through choosing a healthy diet, being physically active and maintaining a healthy body weight – about 84,000 cases per year in the UK.
The charity has launched a campaign, ‘I CAN’, to improve these low levels of awareness and encourage people to take action.
The campaign will help people to stick to healthy New Year’s resolutions that could reduce their cancer risk. People can sign up to receive email tips on weight, diet, alcohol and physical activity by visiting their website.
Amanda McLean, director at World Cancer Research Fund UK, said: "It is worrying that so many people are still not aware that being overweight can increase their chances of developing cancer.
"In fact our research has shown that about 24,000 cancer cases in the UK could be avoided if everyone was a healthy weight.
"This New Year we hope people will get behind our campaign, ‘I CAN’, and make small changes to their lifestyles – they could make a huge difference to their health.
"It doesn’t have to be anything too difficult – cutting down on high calorie foods and sugary drinks, drinking less alcohol, or even 10 to 15 extra minutes each day of physical activities such as brisk walking could all decrease a person’s cancer risk."
When comparing England, Scotland and Wales, the poll showed that Welsh adults are the least aware that being overweight (51% aware), physically inactive (44% aware), eating a poor diet (59% aware) and drinking alcohol (52% aware) all increase the risk of developing cancer.
Regionally, adults in Yorkshire and the Humber are the least aware of the link between physical inactivity and the risk of cancer (59% not aware compared to a national average of 54%) and adults in the West Midlands are the least aware that drinking alcohol (54% not aware compared to a national average of 43%) increases the risk of developing cancer.
Adults in the East of England are the least aware of the cancer risk of eating a poor diet (47% not aware compared to a national average of 40%).