Analysis from Cancer Research UK shows that, by 2035, the UK could see 7,097 cancer deaths every year linked to drinking.
Of these cases, 3,674 will be oesophageal cancer caused by drinking, 1,369 will be bowel cancer and a further 835 will be breast cancer.
The report also forecasts there will be more than 1.2 million hospital admissions for cancer caused by drinking over the 20 years, which will cost the NHS £100 million, on average, every year.
13 ways to help prevent cancer
13 ways to help prevent cancer
Stopping smoking. This notoriously difficult habit to break sees tar build-up in the lungs and DNA alteration and causes 15,558 cancer deaths a year
Avoiding the sun, and the melanoma that comes with overexposure to harmful UV rays, could help conscientious shade-lovers dodge being one of the 7,220 people who die from it
A diet that is low in red meat can help to prevent bowel cancer, according to the research - with 30 grams a day recommended for men, and 25 a day recommended for women
Foods high in fibre, meanwhile, can further make for healthier bowels. Processed foods in developed countries appear to be causing higher rates of colon cancer than diets in continents such as Africa, which have high bean and pulse intakes
Two servings of fruit and three servings of vegetables a day were given as the magic number for good diet in the research. Overall, diet causes only slightly fewer cancer deaths than sun exposure in Australia, at 7,000 a year
Obesity and being overweight, linked to poor diet and lack of exercise, causes 3,917 deaths by cancer a year on its own
Dying of a cancer caused by infection also comes in highly, linked to 3,421 cancer deaths a year. Infections such as human papilloma virus - which can cause cervical cancer in women - and hepatitis - can be prevented by vaccinations and having regular check-ups
Cutting back on drinks could reduce the risk of cancers caused by alcohol - such as liver cancer, bowel cancer, breast cancer and mouth cancer - that are leading to 3,208 deaths a year
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Sitting around and not getting the heart pumping - less than one hour's exercise a day - is directly leading to about 1,800 people having lower immune functions and higher hormone levels, among other factors, that cause cancers
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Hormone replacement therapy, which is used to relieve symptoms of the menopause in women, caused 539 deaths from (mainly breast) cancer in Australia last year. It did, however, prevent 52 cases of colorectal cancers
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Insufficient breastfeeding, bizarrely, makes the top 10. Breastfeeding for 12 months could prevent 235 cancer cases a year, said the research
Oral contraceptives, like the Pill, caused about 105 breast cancers and 52 cervical cancers - but it also prevented about 1,440 ovarian and uterine (womb) cases of cancer last year
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Taking aspirin also prevented 232 cases in the Queensland research of colorectal and oesophagal cancers - but as it can also cause strokes, is not yet recommended as a formal treatment against the risk of cancer
Scientists are still researching how alcohol can lead to cancer. One theory is that alcohol damages DNA.
Evidence suggests that the more alcohol a person drinks, the higher their risk of cancer.
In January, the UK's chief medical officers said no level of regular drinking is without risks to health.
They said men should consume no more than 14 units of alcohol per week, down from the previous 21 units, bringing them into line with the recommendation for women.
Modelling suggests that, compared with non-drinkers, women who regularly drink two units a day have a 16% increased risk of developing breast cancer and dying from it.
But those who regularly consume five units a day have a 40 per cent increased risk.
For every 1,000 women who do not drink, 109 will develop breast cancer. This rises to 126 women for those who drink 14 units or less per week, and 153 women for those who drink 14 to 35 units a week.
Alison Cox, director of prevention at Cancer Research UK, said of the new data: "These new figures reveal the devastating impact alcohol will have over the coming years.
"That's why it's hugely important the public are aware of the link between alcohol and cancer, and what they can do to improve their risk.
"If we are to change the nation's drinking habits and try to mitigate the impact alcohol will have, then national health campaigns are needed to provide clear information about the health risks of drinking alcohol."
The new report also looks at minimum pricing for a unit of alcohol in England.
It found that, over 20 years, a 50p minimum price per unit of alcohol could cut deaths linked to alcohol by around 7,200, including around 670 cancer deaths. It would also reduce health costs by £1.3 billion, it said.
Professor Sir Ian Gilmore, chairman of the Alcohol Health Alliance, said: "These latest figures show the serious consequences for individuals, the NHS and society if the UK Government continues to ignore the consequences of the nation's drinking.
"In particular they reinforce the need for a minimum unit price for alcohol.
"It is clear from the report that it will save lives, including those lost to cancer, and ease the burden on our health service.
"Importantly, a minimum unit price will do this while leaving moderate drinkers and prices in pubs and bars unaffected."
Caroline Moye, head of the World Cancer Research Fund, said: "This study further adds to the evidence that alcohol is having a deadly effect on the nation.
"Our own research shows that alcohol increases the risk of a number of common cancers including breast, mouth and throat.
"In fact, every year around 21,000 cancer cases could be avoided in the UK if no-one drank.
"After not smoking and being a healthy weight, not drinking alcohol is the best thing people can do to help reduce their cancer risk."
Dave Roberts, director general of the Alcohol Information Partnership, which receives funding from drinks firms including Diageo, Campari and Bacardi, questioned the figures, adding: "According to the Global Burden of Disease Study 2015, the UK overall alcohol-attributable cancer death rate has fallen by 7.5 per cent since 2005."
He added: "Alcohol consumption in the UK has fallen over the past decade with a 32 per cent fall in harmful drinking among young people and a 61% fall in the number drinking alcohol in the past five days.
"An increased risk of cancer is always serious. However, the data suggests that to reduce the risk of cancer, adults should consume alcohol within government guidelines, avoid smoking, eat well and exercise."
- More about:
- Cancer Research Uk
- World Cancer Research Fund
- Alcohol Health Alliance
- Alcohol Information Partnership