The survey of 1,000 children in England aged eight to 13 years also finds that 64% of children whose parents smoke would rather their parents quit than give them more pocket money.
Nine out of 10 children surveyed have never tried a cigarette, with 91% of these believing that they will never try one.
The results coincide with a DoH advertising campaign aimed at getting loved ones to stop smoking. It features real children, not actors, talking about how concerned they are about their parents' smoking.
Public health minister Gillian Merron said: ‘You are four times more likely to quit if you use the free NHS stop smoking service. The facts are clear - every week 2,000 people die from smoking-related diseases, which has a devastating effect on children's lives.'