Many parents are ignoring warnings about smoking near their children, NHS research suggests.
TV advert on the dangers of smoking near children
Almost two-fifths (39%) of teenagers quizzed were exposed to smoke in the home when younger, while 13% were exposed to it in cars.
The poll of 500 children coincides with the relaunch of adverts showing the risks of smoking near children.
They were highlighted by Sol Rickman, five, who has the "lungs of a pensioner" due to his mother's habit.
Sol developed breathing difficulties and when surgeons operated on him they said his lungs looked like those of a lifelong smoker. His mother has since kicked her 20-a-day habit.
The NHS television adverts show young children and babies appearing to breathe out tobacco smoke, while new print adverts show a child's bottle filled with smoke.
In the ICM poll, almost half (49%) of teenagers said their parents or relatives smoked near them when they were younger - 45% wished they had not.
Other research showed almost half of adult smokers (45%) admitted smoking in the car with children present, while almost a third (28%) smoked in the same room.
Yet, of the 1,078 adult smokers questioned for the Central Office of Information study last year, 60% said they disapproved of smoking near children.
Smoking around children has been linked to an increased likelihood of cot death, bacterial meningitis, asthma attacks and other breathing problems.
Children who live with smokers are also more likely to need tonsils or adenoids removed.
Public health minister Caroline Flint said: "It is important that we increase the public's awareness of the real health risks to children from second-hand smoke - not merely the discomfort caused by being in a smoky atmosphere."
Jean King, of the charity Cancer Research UK, said: "These findings highlight the grave and entirely unnecessary danger many children are exposed to in secondhand smoke.
"It is shocking that so many parents smoke near their children when the dangers are so well known."
Donna Covey, chief executive of the Asthma UK charity, said: "I think parents who smoke would be truly shocked if they knew how much their habit can harm their children.
"Young children are very sensitive to cigarette smoke - it can trigger asthma attacks and cause asthma in children who were previously healthy.
"More and more research is showing that children of smokers suffer even if their parents don't smoke in the same room as them.
"The best thing a smoking parent can do for their child is to quit."
NHS Smoking Helpline adviser Alexia Paterson said it was "worrying" that many children quizzed said their parents smoked in a car while they were there.
"You can reduce children's travel sickness and make a positive difference to their health by avoiding smoking when they travel with you."