Nine out of ten respondents thought that a child's risk of getting chest infections was increased by passive smoking and over 80% thought that passive smoking would increase a non-smoking adult's risk of lung cancer, bronchitis and asthma.
The anti-smoking lobby said the statistics proved that tough measures to clamp down on smoking in the workplace would carry the support of the public.
Data from the Office for National Statistics shows that the percentage of people in favour of restrictions at work rose from 81% in 1996 to 85% in 1999.
Support for similar restrictions in restaurants rose from 85% in 1996 to 88% in 1999.
The proportion of people who favour smoking restrictions in pubs has also risen over the same time period, from 48% to 54%.
The ONS survey was carried out on behalf of the Department of Health.
Other key findings include:
The survey found that most people were aware of the health impact of passive smoking.
Nine out of ten respondents thought that a child's risk of getting chest infections was increased by passive smoking and over 80% thought that passive smoking would increase a non-smoking adult's risk of lung cancer, bronchitis and asthma.
More than half of respondents who did not smoke said they would mind if other people smoke near them.
Some 60% of smokers said they do not smoke at all when they are in a room with a child.
Many smokers also modify their smoking in the company of adult non-smokers - 49% do not smoke at all and 34% smoke fewer cigarettes.
Measures under consideration
Clive Bates, director of the anti-smoking charity Action on Smoking and Health, said the statistics showed that the public would support measures to restrict smoking in the workplace proposed by the Health and Safety Commission and currently under consideration by the government.
Mr Bates accused ministers of wavering on the issue, and warned any attempt to introduce a voluntary code of conduct would be a waste of time.
He told BBC News Online: "Number Ten is scared of accusations that the measures would place additional burdens and red tape on small businesses.
"I fear the government is thinking about how best to craft its anti-red tape image, rather than about doing the right thing for health reasons."
Juliette Torres, of the smokers' rights group FOREST, told BBC News Online: "Smokers have to be aware that restrictions are part and parcel of every day life.
"We promote the idea that both smokers and non-smokers should be catered for."
Ms Torres said the statistics also showed that smokers were modifying their behaviour to take into consideration the atttitudes of others.
"If only the vehement anti-smokers were similarly minded."