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.
Even former drinkers who have now quit are still at risk of cancer, including of the oesophagus, breast, mouth and bowel.
NHS 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 latest research, published in the British Medical Journal (BMJ), found cancer risks at even lower levels.
Experts analysed data from eight European countries, including the UK, 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. In the UK, one unit is defined as 8g of alcohol.
The research found that men in Germany were the most likely to exceed 24g a day (43.8% of the male population), followed by Denmark (43.6%) and the UK (41.1%). Among women, Germans were most likely to drink over 12g a day (43.5% of women), followed by those in Denmark (41%) and the UK (37.7%).
Cancers of the pharynx, oesophagus and voice box were most commonly caused by alcohol, followed by liver cancer. Even more cancers were thought to be partly attributable to drinking, and for every additional drink a day, the risks went up.
Cancer Research UK, which helped fund the study, said the findings showed that alcohol causes at least 13,000 cases of cancer a year in the UK.
The Department of Health, which is set to publish a new alcohol strategy in the summer, said it is taking "tough" action to tackle problem drinking, including plans to stop supermarkets selling cheap alcohol and the introduction of more stringent licensing laws.