Of the 1,000 parents surveyed, 86 per cent said they would support such a ban when passengers are under 18 years old.
Support was also high among parents who smoke, with 83 per cent of this group backing such a ban.
Among former smokers surveyed, five per cent admitted to smoking in the car with the window open when travelling with their children and this figure rose to 13 per cent among those parents who currently smoke.
Half of smokers and former smokers surveyed said they had exposed their children to second-hand smoke.
Dame Helena Shovelton, chief executive of the British Lung Foundation, said: "Parents are sending a clear message to the government that smoking in cars with children under the age of 18 should be banned.
"Smoking just one cigarette, even with the car window open, creates a greater concentration of second-hand smoke than a whole evening's smoking in a pub or a bar. A ban on smoking in the car with children would prevent some of the 22,000 new cases each year of asthma, caused as a direct result of passive smoking."
The survey has been carried out as part of a campaign by the charity surrounding the dangers of passive smoking. This includes a national poster advertising campaign, featuring an image of a child being forced to smoke a cigarette in a car by an adult, with the caption "when you smoke in the car, they smoke".
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Smoking in cars carrying children should be banned, says survey of parents
Smoking in cars when children are passengers should be banned, according to a survey of parents carried out by the British Lung Foundation.