A study on more than 1.2 million women in the UK finds that alcohol consumption may account for nearly 13% of all breast, liver, rectal, and upper digestive tract cancers in women.  Even relatively small amounts of alcohol appear to raise cancer risk.  
More Information:
Compared to those drinking 2 or fewer alcoholic beverages per week, those drinking up to 6 alcoholic beverages had a 2% greater risk for cancer in general.
Those drinking 7-14 drinks per week had a 5% increased risk for cancer.
And those consuming 15 or more per week had a 15% increased risk for cancer.  
NBC Nightly News (watch to the end of the video) reported that a “study of over 1.3 million women in Britain … found even a drink a day seems to increase risk of some cancers in women, primarily breast, throat, rectum, and liver.” 
And, “because American women drink a lot like British women … five percent of all cancers in middle-aged women may in fact be due to alcohol.”
On its website, ABC News reported, “Even moderate alcohol consumption of more than two drinks a week may raise the risk of cancer,” according to a study conducted by researchers at Oxford University. 
The study of “more than 1.2 million women in the United Kingdom” revealed that “drinking alcohol may account for about 13 percent of all breast, liver, rectal, and upper digestive tract cancers in women.”
For the study, appearing in the Journal of the National Cancer Institute, “the women completed a questionnaire” at enrollment and at three years, “which included information on how much wine, beer, and spirits they drank on average each week,” 
MedWire added. The “incidence of cancer” was then “compared…seven years after enrollment among women consuming different levels of alcohol.” 
The researchers found that “68,775 women were diagnosed with cancer,” and “the risk of any cancer….rose with increasing alcohol consumption” among those who drank. 
In fact, “each additional drink consumed per day on a regular basis” was “associated with 11 additional breast cancers per 1,000 women up to the age of 75 years.” Notably, “the increased cancer risk did not depend on the type of alcohol, only the amount.”
USA Today says people should decide whether cancer, heart disease pose greater individual risk and editorializes, “A huge British study, reported in the Journal of the National Cancer Institute, found that as little as one alcoholic drink a day increases a woman’s risk of several cancers,” which “seemed to trump findings, going back decades, that moderate drinking can be a benefit by decreasing risk of heart disease.” 
But, “there’s strong evidence for both findings.” 
Furthermore, the British study failed to “calculate the effect on overall death rates,” while other studies “show that moderate drinkers have the lowest mortality rates.” 
USA Today concludes that people should “decide which disease poses a bigger threat in their particular case.”
Another editorial concludes that “there is no level of alcohol consumption that can be considered safe.”  
However, it is interesting to note that non-drinkers had about the same increased risk as those consuming up to 6 drinks per week – a 2% increase in cancer odds compared to those drinking 2 or fewer per week.