There were 1,200 fewer hospital admissions for heart attacks in England in the year after July 2007 - when the smoking ban came in, a study suggests.
The 2.4% drop was much more modest than that reported in some areas where similar bans have been introduced, but may still have saved the NHS over £8m.
Researchers said even a small reduction had "important public health benefits".
The Bath team analysed English hospital admissions between 2002 and 2009, the British Medical Journal reports.
Separate research by the London Health Observatory carried out on the basis of their figures suggested a saving to the NHS of £8.4m in the first year after the ban on smoking in public indoor spaces was introduced in England.
Similar legislation had already been introduced in Scotland, Wales and Northern Ireland.
Focusing on a population of 49m, the Bath study, commissioned by the Department of Health, was the largest, most comprehensive study to date on the effects of smoke-free legislation anywhere in the world.
It took into account a variety of factors which can influence heart attacks - from the weather to influenza rates.
The theory is that non-smokers' exposure to smoke has the same effect on the heart as if they were light smokers, and can trigger acute coronary problems - meaning that at least some of the impact of a smoking ban should become apparent relatively quickly.
Studies have painted a mixed picture of the effects of such bans - with one from the US reporting a 40% drop in the number of hospital admissions for heart attacks. But others, notably those from New Zealand, and Piedmont, Italy, found no overall reduction.
Research from Scotland, where a ban was introduced in March 2006, reported a 17% decrease in heart attack admissions in the year after its ban.
But the team of researchers from Bath University did not uncover as large a drop.
They said heart attack admissions had been falling in England in the run-up to the ban, making any subsequent decline far less dramatic.
They argued that one of the reasons for this fall prior to the 2007 legislation was the fact that many establishments had become smoke-free in anticipation of the ban.
But they also suggested that their study, in which as many influencing factors as possible were accounted for, was the most rigorous to date and therefore less likely to inflate the impact.
The fall recorded was nonetheless an important one, and even greater benefits were likely to emerge in years to come, said Dr Anna Gilmore, director of the Tobacco Control Research Group, who led the study.
"Given the large number of heart attack attacks in this country each year, even a relatively small reduction has important public health benefits," she added.
But the researchers cannot say categorically that the drop was down to a reduction in exposure to second-hand smoke, or because fewer people are smoking in the first place. Data on the smoking status of the patients admitted was not available, and the Bath University team intends to look at this next.
Surveys have suggested strong public support for the ban, although last year a cross-party group of MPs argued the laws needed amending to stop pubs losing valuable trade from smokers.
Supporters of the ban welcomed the study.
Professor John Britton of the Royal College of Physicians said the findings demonstrated "once again the importance of preventing passive smoking.
"We urge the government to take further steps to close the remaining loopholes in the existing smoking laws, and to act to prevent the continued exposure of children to passive smoking in the home."
But smokers rights campaigners said the findings should be treated with caution.
"The number of emergency heart attack admissions had been falling for several years, even before the smoke-free legislation, so what we are seeing is part of a trend that has nothing to do with the smoking ban," said Simon Clark, director of Forest.
"This study is designed to show the benefits of prohibition. What is doesn't show is the misery that has been heaped on hundreds of thousands of people by an unnecessarily harsh and divisive piece of legislation."