For some types of cancer, the rates are significantly higher, it said.
In 2008, for men, 44, 25 and 33 percent of upper digestive track, liver and colon cancers respectively were caused by alcohol in six of the countries examined, the study found.
The countries were Britain, Italy, Spain, Greece, Germany and Denmark.
The study also showed that half of these cancer cases occurred in men who drank more than a recommended daily limit of 24 grammes of alcohol, roughly two small glasses of wine or a pint of beer.
The cancer rates for women in the same countries, along with the Netherlands and France, was 18 percent for throat, mouth and stomach, 17 percent for liver, five percent for breast and four percent for colon cancer.
Four-fifths of these cases were due to daily consumption above recommended limits, set for women at half the level of men.
The International Agency for Research on Cancer (IARC) has long maintained that there is a causal link between alcohol consumption and cancers, especially of the liver, colon, upper digestive tract and, for women, breast.
But few studies have tried to connect the dots across a large population between cancer rates and total alcohol consumption, or the proportion of the disease burden occurring in people who drink more than guidelines would allow.
"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," said Madlen Schutze, an epidemiologist at the German Institute of Human Nutrition in Potsdam and lead author of the study.
The findings also suggest that the limits set by many national health authorities may not be stringent enough to avoid the disease, she said.
"Even more cancer cases would be prevented if people reduced their alcohol intake to below recommended guidelines or stopped drinking alcohol at all," she said in a statement.
The results, published in the British Medical Journal (BMJ), are drawn from the so-called EPIC cancer survey of 363,000 men and women who have been tracked since the mid-1990s.
Other risk factors that might have also led to cancer -- especially smoking and obesity -- were taken into account, the researchers said.
Nearly 44 percent of men in Germany exceeded the 24-gramme daily limit, followed by Denmark (43.6 percent) and Britain (41.1 percent).
Among women, Germany still topped the list, with 43.5 percent of women there exceeding limit, with Denmark (41 percent) and Britain (37.7 percent) coming in second and third.