The ICM survey found 46% had experienced them intoxicated.
It also found four in 10 (42%) parents say their child has seen them or their partner drunk. Three in 10 children (29%) say they have seen their parents drunk on more than one occasion, according to the study for the alcohol education charity Drinkaware.
However, 72% of parents said they feel confident talking to their child about drinking and 75% believe they are best placed to do so.
Elaine Hindal, chief executive of Drinkaware, said: "While setting rules about alcohol and speaking to children about the risks is a positive step, equally important is that parents understand their significant influence as role models and feel confident to set a good example."