Up to one in 10 cancers in men and one in 33 in women across Western Europe could be caused by drinking, according to new research.
While even small amounts increases the risk, drinking above recommended limits may be responsible for the majority of cancer cases linked to alcohol, experts said.
And even former drinkers who have now quit are still at risk of cancer, including of the oesophagus, breast, mouth and bowel.
The new research, published in the British Medical Journal, found cancer risks at even lower levels.
Experts analysed data from eight European countries and worked out what proportion of men and women were drinking above guidelines of 24g of alcohol a day for men and 12g a day for women.
Men and women in Germany, Denmark and the Uk were most likely to exceed recommended guidelines, according to the study.
Overall, 3 per cent of cancers in men were linked to drinking less than 24g of alcohol a day but more than 18 per cent were down to drinking more than 24g a day.
In women, 1 per cent of cancers were down to drinking less than 12g of alcohol a day while 4 per cent were due to drinking more than 12g of alcohol daily.
Some 17 per cent of bowel cancers in men were linked to drinking as were 4 per cent of cases in women.
And 5 per cent of breast cancers in women were also down to drinking, the study showed.
Even more cancers were thought to be partly attributable to drinking, and for every additional drink a day, the risks went up.
The authors, from universities and hospitals across Europe, said: "Our data show that many cancer cases could have been avoided if alcohol consumption is limited to two alcoholic drinks per day in men and one alcoholic drink per day in women, which are the recommendations of many health organisations.
"And even more cancer cases would be prevented if people reduced their alcohol intake to below recommended guidelines or stopped drinking alcohol at all."
The research is part of the European Prospective Investigation of Cancer (EPIC), one of the largest-ever studies into the links between diet and cancer.
It involved more than 360,000 men and women who were mostly aged 35 to 70 at the start of the study.
Their alcohol intake at recruitment stage in the 1990s was noted, and the follow-up examined how many developed cancer.
Alcohol creates a chemical when it is broken down by the body which can damage DNA and increase the risk of cancer.
Naomi Allen, from 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 10 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."
The study involved data from France, Italy, Spain, the UK, the Netherlands, Greece, Germany and Denmark.
Overall, in 2008, current and former alcohol consumption caused about 57,600 cases of cancer of the upper digestive tract, bowel and liver in men across Denmark, Greece, Germany, Italy, Spain and the UK, it showed.
More than half of these cases were caused by drinking more than two alcoholic drinks per day.
Across all eight countries, some 21,500 cases of upper digestive tract, liver, bowel and breast cancer in women were caused by drinking, of which over 80 per cent was due to more than one drink of beer, wine, or spirits per day.