The Ipsos MORI survey found the behaviour of friends is also a powerful factor in predicting drinking habits.
The more time teenagers spend with friends, the more likely they are to drink alcohol, it suggested.
In a survey of 5,700 children aged 13 to 16, carried out for the Joseph Rowntree Foundation, researchers found one in five claimed to have been drunk by the time they were 14.
By the age of 16, half of those questioned said they had been drunk.
Influences But the study also looked at what influences excessive teen drinking - and the habits of parents seem to be particularly powerful.
The odds of a teenager getting drunk repeatedly is twice as great if they have seen their parents under the influence, even if only a few times.
And the authors say that parental supervision is also important - if parents don't know where their children are on a Saturday night, or let them watch 18 certificate films unsupervised, they are more likely to have had an alcoholic drink.
Claire Turner Joseph Rowntree FoundationBoth what parents say, and how they behave, have a strong impact on their teenagers' drinking, drinking regularly, and drinking to excess”
Teenagers' friends also have a significant impact on drinking behaviour.The odds of a teenager drinking to excess more than double if they spend more than two evenings a week with friends.
Spending every evening with friends multiplies the odds of excessive drinking more than four times.
Pamela Bremner from Ipsos MORI, the lead author of the report, said: "For the first time in the UK, this study ranks what most influences young people's drinking behaviour.
"It found that the behaviour of friends and family is the most common influential factor in determining how likely and how often a young person will drink alcohol."
Researchers found mixed messages about the ideal age and ways of introducing teenagers to alcohol.
Generally, those introduced to alcohol at a very young age had greater odds of being a regular drinker and of having been drunk multiple times.
But there were differences in the pattern for young people of different ages.
"This research shows that parents can have more influence on their teenagers' behaviour than perhaps many assumed," said Claire Turner, Programme Manager for the Joseph Rowntree Foundation.
"Both what parents say, and how they behave, have a strong impact on their teenagers' drinking, drinking regularly, and drinking to excess.
"Being introduced to alcohol at a very young age - for example, under 10 years old - makes it more likely that they will drink and drink to excess as teenagers.
"But there are differences in patterns across the group. So for the older teenagers, if they are introduced to alcohol later in life via friends, away from adult supervision, they are also more likely to drink to excess."
Don Shenker, Chief Executive of Alcohol Concern, said the report confirms that from the beginning of a child's life parents have a strong influence on their children's future drinking patterns.
"Parents have to realise and accept that whether intended or not, their own attitudes towards drinking, their own rate of drinking and any drunkenness are clear signals to children that this is acceptable and standard behaviour.
"In addition parents must accept that allowing children to drink unsupervised can increase the risk of their children being drunk and this can have harmful consequences.
"Government ministers must also look at some of the causes of why it is so easy for children to obtain alcohol, usually from the home.
"Government should look to see if they've done everything they can to stop the large supermarkets from continuing to heavily promote cheap alcohol which incentivises more alcohol purchases and therefore results in more alcohol being stored in the home."
The Royal College of Physicians also said it was not surprised that being able to access alcohol easily was an important influencing factor on current drinking patterns and drunken-ness of teenagers.
A statement said: "This shows that the government needs to concentrate on increasing the price per unit of alcohol and reducing its availability as their main priorities, and in addition to increase education and national campaigns for both young people and their families on the dangers of alcohol."