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.
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 per cent 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.”
Caroline Moye, head of the World Cancer Research Fund, said: “After not smoking and being a healthy weight, not drinking alcohol is the best thing people can do to help reduce their cancer risk.”