One in 10 cancers in men and one in 33 in women across Western Europe are caused by drinking, according to new research.
While even small amounts increases the risk, drinking above recommended limits causes 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 guidelines are that men should drink no more than three to four units a day while women should not go over two to three units a day.
But 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 the guidelines.
Cancers of the pharynx, oesophagus and voice box were most commonly caused by alcohol, followed by liver.
Overall, 3pc of cancers in men were linked to drinking less than 24g of alcohol a day but more than 18pc were down to drinking more than 24g a day.
In women, 1pc of cancers were down to drinking less than 12g of alcohol a day while 4pc were due to drinking more than 12g of alcohol daily.
Some 17pc of bowel cancers in men were linked to drinking as were 4pc of cases in women.
And 5pc 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 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, involving 360,000 people.
Alcohol creates a chemical when it is broken down by the body which can damage DNA and increase the risk of cancer.