Three-quarters of people in the UK do not know about the link between obesity and the 10 different cancers it can cause, research shows.
Fat is as dangerous as cigarette smoking in reproductive cancers such as cancer of the womb, which less than a quarter of people know is linked to being overweight, Cancer Research UK said in a report looking at obesity and cancer nationally for the first time.
If obesity is not tackled there will be 670,000 additional cases of cancer over the next 20 years which could cost the health service around £2.5 billion, the charity warned.
The condition is the second most common cause of preventable cancer after smoking, and is probably responsible for more than 18,000 cases a year.
But 78% did not know obesity is linked to ovarian or womb cancer, more than two-thirds (69%) were unaware it can lead to breast cancer, and more than half (53%) did not know of the link to cancer of the pancreas.
People who were less well-off were less likely to be aware of the link than those in the higher social groups, according to the online survey of 3,293 people by the Policy Research Centre for Cancer Prevention at Cancer Research UK.
Professor Peter Johnson, chief clinician for Cancer Research UK, said people should stop perceiving cancer as "an inevitability" and ask themselves what they could do to minimise their chances - an "under-recognised question".
He said: "Historically there has been a sense that there was nothing one could do about the risk of getting cancer, but as time goes on it's clear that there are more and more things we can do, and maintaining a healthy body weight and reducing obesity are clearly two very important components of that."
While details of the link between being overweight and developing cancer are still being probed, it is thought storing excess fat can increase the level of sex hormones including oestrogen, which can make cells multiply faster in the womb and the breast.
Womb cancer ranks highest in its association with obesity, and a morbidly obese woman may have a 15% to 20% lifetime risk of womb cancer - equivalent to the risk of lung cancer in a lifetime heavy smoker.
Post-menopausal, overweight women are particularly at risk because their bodies no longer produce the natural antagonist to oestrogen that is released during the second half of the menstrual cycle, so the womb lining can continue to thicken.
Excess fat also causes insulin levels to rise, which can tell cells to divide, and thereby increase, more rapidly, while special immune cells in fat tissue can lead to chronic inflammation which can aid the growth of cancer.
The charity admitted obesity is a "loaded and contentious" topic that many people - including GPs - have strong opinions about. It noted doctors can be reluctant to bring up obesity concerns with patients attending an appointment for a separate matter for fear of damaging the relationship.
A lot of people did not identify themselves are obese, which could be down to obesity being widely portrayed as an extreme which does not resonate with people with a lower level of obesity.
It praised the recent sugar tax levy but warned much more needs to be done to tackle the crisis at its root, with one in three children leaving primary school overweight or obese.
The Government should restrict marketing by ensuring junk food adverts are not aired on television before the 9pm watershed, and set mandatory targets for the food and drinks industry to reduce sugar and fat in products, the charity recommended.
People should also take individual responsibility, and the charity acknowledged that the threat of cancer could be enough to kick-start obese and overweight people into taking steps to manage their problem.
A Department of Health spokesman said: "Being overweight can increase the risk of developing cancer and this is one of the reasons why we are taking firm action to tackle the nation's obesity crisis.
"Our obesity plan is world-leading, with more far-reaching and comprehensive measures than anything pursued by any other western government.
"Nevertheless, we will measure progress carefully and do not rule out further action if results are not seen."
Public Health England said it would be launching an "ambitious programme" to challenge the food industry to remove at least 20% of the sugar in its products by 2020.