Cancer Research UK-funded researchers also show that alcohol has the biggest effect on cancers of the mouth, food-pipe, voice-box and pharynx. More than 6000 of these cancers were caused by drinking.
Alcohol also causes more than 3000 colorectal cancers and about 2500 breast cancers per year.
Study leaders looked at how different levels of drinking affect the risk of cancer, and combined them with figures on how much British people drink.
The research* is part of ongoing work by the European Prospective Investigation of Cancer (EPIC) - a Cancer Research UK co-funded study and one of the largest studies into the links between diet and cancer.
Alcohol is known to increase the risk of several types of the disease including mouth, throat, bowel, liver and breast cancers. When alcohol is broken down by the body it produces a chemical which can damage DNA, increasing the chance of developing cancer.
However, the cancer risk increases with every drink, so even moderate amounts of alcohol - such as a small drink each day - increases the risk of these cancers.
Naomi Allen, a Cancer Research UK epidemiologist based at Oxford University, who works on the EPIC study, said: "This research supports existing evidence that alcohol causes cancer and that the risk increases even with drinking moderate amounts.
"The results from this study reflect the impact of people's drinking habits about ten years ago. People are drinking even more now than then and this could lead to more people developing cancer because of alcohol in the future."
Government figures from the Office of National Statistics, published last week, showed that an increasing number of women are drinking high amounts of alcohol, well over the recommended limit for a week.
This is of concern as previous evidence shows that drinking one small drink a day regularly can significantly increase the risk of breast cancer, the most common cancer in women in the UK.
Sara Hiom, director of health information at Cancer Research UK, said: "Many people just don't know that drinking alcohol can increase their cancer risk.
"In the last ten years, mouth cancer has become much more common and one reason for this could be because of higher levels of drinking - as this study reflects.
"Along with being a non-smoker and keeping a healthy bodyweight, cutting back on alcohol is one of the most important ways of lowering your cancer risk.
"Keeping alcohol intake to a maximum of one small drink a day for women and two small drinks per day for men can have a real impact."
Source: Cancer Research UK
