The globe is facing a "tidal wave" of cancer, and restrictions on alcohol and sugar need to be considered, say World Health Organization scientists.
It predicts the number of cancer cases will reach 24 million a year by 2035, but half could be prevented.
The WHO said there was now a "real need" to focus on cancer prevention by tackling smoking, obesity and drinking.
The World Cancer Research Fund said there was an "alarming" level of naivety about diet's role in cancer.
Fourteen million people a year are diagnosed with cancer, but that is predicted to increase to 19 million by 2025, 22 million by 2030 and 24 million by 2035.
The developing world will bear the brunt of the extra cases.
Chris Wild, the director of the WHO's International Agency for Research on Cancer, told the BBC: "The global cancer burden is increasing and quite markedly, due predominately to the ageing of the populations and population growth.
"If we look at the cost of treatment of cancers, it is spiralling out of control, even for the high-income countries. Prevention is absolutely critical and it's been somewhat neglected."
The WHO's World Cancer Report 2014 said the major sources of preventable cancer included:
- Obesity and inactivity
- Radiation, both from the sun and medical scans
- Air pollution and other environmental factors
- Delayed parenthood, having fewer children and not breastfeeding
For most countries, breast cancer is the most common cancer in women. However, cervical cancer dominates in large parts of Africa.
The human papillomavirus (HPV) is a major cause. It is thought wider use of the HPV and other vaccines could prevent hundreds of thousands of cancers.
One of the report's editors, Dr Bernard Stewart from the University of New South Wales in Australia, said prevention had a "crucial role in combating the tidal wave of cancer which we see coming across the world".
Dr Stewart said human behaviour was behind many cancers such as the sunbathe "until you're cooked evenly on both sides" approach in his native Australia.
He said it was not the role of the International Agency for Research on Cancer to dictate what should be done.
But he added: "In relation to alcohol, for example, we're all aware of the acute effects, whether it's car accidents or assaults, but there's a burden of disease that's not talked about because it's simply not recognised, specifically involving cancer.
"The extent to which we modify the availability of alcohol, the labelling of alcohol, the promotion of alcohol and the price of alcohol - those things should be on the agenda."
He said there was a similar argument to be had with sugar fuelling obesity, which in turn affected cancer risk.
Meanwhile, a survey of 2,046 people in the UK by the World Cancer Research Fund (WCRF) suggested 49% do not know that diet increases the risk of developing cancer.
A third of people said cancer was mainly due to family history, but the charity said no more than 10% of cancers were down to inherited genes.
Amanda McLean, general manager for the WCRF, said: "It's very alarming to see that such a large number of people don't know that there's a lot they can do to significantly reduce their risk of getting cancer.
"In the UK, about a third of the most common cancers could be prevented through being a healthy weight, eating a healthy diet and being regularly physically active.
"These results show that many people still seem to mistakenly accept their chances of getting cancer as a throw of the dice, but by making lifestyle changes today, we can help prevent cancer tomorrow."
It advises a diet packed with vegetables, fruit, and wholegrains; cutting down on alcohol and red meat; and junking processed meat completely.
Dr Jean King, Cancer Research UK's director of tobacco control, said: "The most shocking thing about this report's prediction that 14 million cancer cases a year will rise to 22 million globally in the next 20 years is that up to half of all cases could be prevented.
"People can cut their risk of cancer by making healthy lifestyle choices, but it's important to remember that the government and society are also responsible for creating an environment that supports healthy lifestyles.
"It's clear that if we don't act now to curb the number of people getting cancer, we will be at the heart of a global crisis in cancer care within the next two decades."