Regularly drinking two large glasses of wine or two strong pints of beer a day triples the risk of developing mouth cancer, a new Government campaign will say.
The adverts aim to show that drinking just over the recommended daily limit for alcohol increases the risk of serious health problems.
NHS recommendations are that men should not regularly drink more than three to four units a day, while women should not regularly drink more than two to three.
Adverts will run under the Change4Life banner and people will be able to access a new online calculator to work out how much they are drinking.
Two million leaflets will also be made available to Change4Life supporters and health professionals across England.
Drinkers will be encouraged to cut down through measures such as having alcohol-free days, not drinking at home before going out, swapping to low or alcohol-free drinks and using smaller glasses.
The campaign follows a survey of more than 2,000 people which found 85% do not realise that drinking over recommended limits increases the risk of developing breast cancer.
Some 65% were unaware it increases the risk of bowel cancer, 63% did not know about a raised risk of pancreatitis and 59% did not realise excess drinking increases the risk of mouth, throat and neck cancer.
Some 30% did not realise that drinking just over the limits increases the risk of high blood pressure and 37% did not realise it can impact on fertility.
Health Secretary Andrew Lansley said: "It's crucial we support people to know about how drinking too much poses risks to their health and how they can take control of their drinking.
"It can be easy to slip into the habit of having a few extra drinks each day, especially when drinking at home. But there can be serious health risks. Don't let drinking sneak up on you."
The issue of how to tackle alcohol abuse has proved controversial for the Government.
Last year, six major health organisations refused to back the public health responsibility deal, saying the Government was allowing the drinks industry to dictate health policy.
Under the deal, drink producers and retailers, including Diageo, Carlsberg and Majestic Wine, have pledged to provide clear unit labelling, support awareness campaigns and develop a new sponsorship code on responsible drinking.
But Alcohol Concern, the British Medical Association (BMA), the Royal College of Physicians, the British Association for the Study of the Liver, the British Liver Trust and the Institute of Alcohol Studies refused to support the deal.
Don Shenker, chief executive of Alcohol Concern, said it represented "the worst possible deal for everyone who wants to see alcohol harm reduced", with no sanctions if industry failed to meet the pledges, while the BMA said the Government had "chosen to rely on the alcohol industry to develop policies".
Alcohol Concern welcomed the new campaign but said "to a great extent this is the easy bit".