The legal age limit for buying alcohol should be more rigorously enforced, a survey for the BBC has found.
The public is split over drinking promotions
It discovered 87% wanted the government should put more funding into initiatives to ensure that under-18s cannot buy alcohol.
Just under 80% wanted more safe drinking campaigns - but two thirds still said it was up to individuals to decide how much they drank.
ICM conducted a phone poll of 1,010 adults in England, Wales and Scotland.
Just under 60% felt the government should not interfere except to inform people of the risks of drinking too much.
The findings once again show people want action on public health issues - but they still want to retain choice about their own actions.
People surveyed for the BBC Healthy Britain poll were split almost equally over whether drinks promotions, such as two-for-one offers should be banned, while just over a third believe taxes on alcohol should be increased to discourage excessive drinking.
A minority - 15% - felt people could be discouraged from excessive drinking by moving towards making alcohol an illegal drug, with twice as many people in social classes DE backing the idea than in AB.
But almost a quarter of all those surveyed felt the age at which people can buy alcohol should be increased to 21 or over.
Three-quarters felt parents who consistently allow their children to drink excessively should ultimately face prosecution, in a bid to tackle under-age drinking.
Other findings of the poll were:
42% think the government should relax licensing laws for pub, clubs and restaurants; 51% think it should tighten licensing laws.
Non-drinkers are more supportive of tightening than drinkers - 61% to 40%.
Over 65s are more in favour of tightening licensing laws than 18-24s - 60% support tightening versus 42% of 18-24s.
Men are more in favour of relaxing licensing laws than women (52% to 32%).
A higher percentage of lower income groups oppose relaxation of licensing laws - 62% of people in social class DE support tightening versus 41% of people in social class AB.
Richard Phillips, Acting Chief Executive of Alcohol Concern, added: "The poll suggests that the public does recognise the problems of alcohol misuse and it's encouraging to see that people want the government to take action.
"On the other hand, people tend to accept changes that affect others but not those that affect themselves.
"Raising drink prices would for example be an effective way of reducing excessive drinking amongst the young, but no one really likes paying more for their drink so this would make the government very unpopular.
"The fact that the public would support government interventions is a green
light for stronger government action in future."
Dr Peter Tiplady, chair of the British Medical Association's Public Health Committee, said: "Although the BMA does not believe alcohol should be made illegal, the government definitely needs to tackle binge-drinking, particularly among adolescents.
"A large part of the problem is the way the drinks industry targets young people, and a ban on alcohol advertising would help prevent manufacturers from glamorising excessive alcohol consumption.
"It is currently unclear how changes to licensing laws will
affect public health, and once they have been introduced, their impact needs to be thoroughly researched."
Jim Minton, of the Portman Group, which promotes responsible drinking. said: "The law regarding the sale of alcohol to over 18s only should be strictly enforced.
"Most pubs, off licenses and supermarkets act responsibly and do not sell alcohol to under 18s, but we would urge all staff in the licensed trade to routinely ask for Proof of Age to ensure that consumers are over the legal age limit."
He said any retailer who knowingly and persistently sold alcohol to under 18s should be aware they are risking losing their license.
Mr Minton added: "Parents have a vital role to play in educating their children about alcohol. It's important that children grow up able to make responsible choices about drinking, and educating them about alcohol will help ensure this happens."