Alcohol consumption has been linked to 10% of cancers in men and one in 33 in women across Western Europe, according to research.
Experts believe that drinking even small amounts can increase the risk, while drinking above recommended limits leads to most cancer cases linked to alcohol.
Even former drinkers who have since quit are still thought to be at risk of cancer, including bowel, mouth, breast and oesophagus.
Alcohol guidelines from the NHS specify that men should not exceed more than three to four units a day while women are advised not to drink more than two to three units on a daily basis.
The new study, published in the British Medical Journal, discovered 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.
Cancers of the pharynx, oesophagus and voice box were most commonly caused by alcohol, followed by liver.
Overall, 3% of cancers in men were linked to drinking less than 24g of alcohol a day but more than 18% were down to drinking more than 24g a day.
In women, 1% of cancers were down to drinking less than 12g of alcohol a day while 4% were due to drinking more than 12g of alcohol daily.
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."