The research found that the bans were associated with high gains in quit attempts by smokers with low incomes.
The study, published in the American Journal of Epidemiology, linked 25 years of health data collected from young-to-middle-aged smokers to a database on smoking bans.
The data showed that the effects of the smoking ban were not uniform. Overall, the bans appeared to be most effective at reducing smoking risk in people with higher levels of education.
"Our results suggest that smoking bans may help start the process among people with lower socioeconomic status by making them more likely to try to quit smoking, but that more needs to be done to help translate it into successful smoking cessation," said Stephanie Mayne, from the Oxford University Press.
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The study also found that bans reduced the risk of becoming heavy smoker (smoking 10 or more cigarettes - half a pack - a day).
However, the introduction of bans did increase the likelihood of trying to quit among lower income people.
People in the lowest income bracket were about 15 per cent more likely to try to quit if they lived in an area where a ban was introduced.