It found that 19pc of youngsters who had parents drinking over recommended guidelines had been drunk before, compared with 11pc of children whose parents drink below the guidelines or not at all.
Similarly, 21pc of children with heavy-drinking parents drink at least monthly in comparison with just 12pc of youngsters whose parents do not exceed guidelines.
Siobhan McCann, head of campaigns and communications at Drinkaware, said: "Most parents want their children to grow up with a healthy relationship with alcohol and try to set a good example.
"The problem is that some parents drink above the guidelines without realising and this in turn influences their children's attitudes and behaviour.
"When it comes to alcohol, parents have the biggest influence on their children and lots of children would turn to their parents first for advice."
The survey also found that the majority of children had a "sensible" attitude to drink.
More than three-quarters (77pc) of 10 to 17-year-olds think that seeing young people getting drunk is not "cool", while 93pc think it is not okay for children to get drunk once a week. Just over one in 10 children believe it is okay to try getting drunk.
The research also found more than a third (36pc) of parents who drink above the recommended daily guidelines believe they drink within safe limits.