They base their findings on the number of emergency admissions for asthma among adults aged 16 and over in England between April 1997 and December 2010.
Smoking in all public places was banned in July 2007 in England, where the prevalence of asthma is one of the highest in the world, affecting almost 6% of the population.
During the study period, 502,000 adults with asthma were admitted as emergencies. As expected, admissions were higher during the winter months than during the summer, although the numbers of admissions varied widely from region to region.
After taking account of seasonal temperatures, variations in population size, and long term trends in the prevalence of asthma, the figures showed that emergency admissions for the condition fell by 4.9% among adults for each of the first three years following the introduction of the smoking ban.
The percentage drop was similar across all geographical regions of the country.
Across England as a whole, the authors calculate that this adds up to around 1900 fewer such admissions in the year immediately following the ban, with a similar number in each of the two subsequent years.
The authors point out that although these figures are lower than those in other countries where smoking bans have been introduced, this might be because many workplaces in England had already adopted smoke free policies before the nationwide ban took effect.
The authors emphasise that although the association they found was significant, it does not prove that the legislation was responsible for the fall in emergency admissions for asthma. Nevertheless, they point out that their data are consistent with other research linking the smoking ban to measures of improved health, and attribute the association to a reduction in second hand exposure to tobacco smoke.
Furthermore, the size of the study population, plus the efforts to account for other underlying factors, add weight to the findings, they suggest.
"[The study] provides further support to a growing body of national and international evidence of the positive effects that introducing smoke free polices has on public health," they conclude.