Nearly three-quarters of people believe smoking in households with children should be banned, a poll suggests.
Many experts believe passive smoking harms children
The survey, by Developing Patient Partnerships, found 72% of respondents, including 65% of smokers, were in favour of a ban.
However, it also found many people were unaware of the full negative impact of smoking around children in the home.
Doctors say it damages children's health, and increases the likelihood they will become smokers themselves.
More than four out of ten (42%) children live in homes with at least one smoker and a third smoke around children.
The survey also found the vast majority of people were unaware of how rapidly health improves after giving up smoking.
Only 9% were able correctly to say that the health benefits start to kick just 20 minutes after the final cigarette.
Most people (66%) believe that employers should offer smokers support to give up.
Developing Patient Partnerships is offering smokers and their loved ones practical advice on how to quit.
Dr Terry John, DPP spokesman and a GP said: "These results show how strongly people feel about smoking around children in the home.
"Parents need practical help that shows the positive side of quitting and encouraging the whole family to get healthy together rather than a law forcing them not to smoke at home."
Deborah Arnott, director of the anti-smoking ASH, welcomed the move to raise awareness about the health hazards of smoking in the home.
"Although knowledge about the dangers of passive smoking is growing, many people underestimate the harm that it causes, especially to children.
"The only way for parents to protect their children from tobacco smoke is by making their homes entirely smoke free."
Simon Clark, director of the smokers' lobby group FOREST, said: "We dispute the alleged impact of passive smoking but, where children are concerned, it makes sense to err on the side of caution.
"We therefore support moves to discourage people from smoking around children in enclosed spaces.
"However, attempts to demonise parents who smoke are unacceptable. Smoking is a legal habit and tobacco is a legal product."
A Department of Health spokeswoman said a recent advertising campaign had highlighted the dangers of smoking near children.
She said: "Nearly half of adult smokers continue to smoke in the car when children are present and almost one third smoke when their children are in the same room.
"We are keen to increase the public's awareness of these risks and to encourage them to take measures to ensure that fewer children suffer the health problems associated with second-hand smoke."
The poll, by ICM Research, was based on telephone interviews with 1,275 adults.