Cigarette sales in the UK dropped by almost 7% in July compared with the same month last year, research says.
The smoking ban came into effect in England on 1 July
The figures, which include shop sales but not bars or vending machines, come from market research firm AC Nielsen.
Campaigners say it is down to bans on smoking in enclosed public spaces which came into effect in England on 1 July and in Wales three months earlier.
However, tobacco manufacturers said it was too early to tell if the smoking bans were affecting sales.
Martin Dockrell, from anti-smoking group Ash, told BBC News he was not surprised at the figures.
He said: "That's pretty much in line with what happened in Scotland and in Ireland and in New York when they all went smoke-free.
"We saw really quite dramatic declines both in smoking prevalence and in the number of cigarettes smoked.
"Fewer people smoked, and those who did smoke smoked less."
Chris Ogden, of the Tobacco Manufacturers' Association, said a single month was not enough to draw any conclusions.
"One month's figures is insufficient for any sensible market analysis," he said.
"It's also a time when people have been on their summer holidays and bringing cigarettes back in from abroad, which they've purchased more cheaply.
"The weather's been bad so people haven't been smoking outdoors as much as they might.
"But we set this against an overall decline of about 2% a year in sales in the UK, so we're experiencing a steady decline anyway."
Elsewhere in the UK, Northern Ireland went "smoke free" on 30 April this year, and Scotland took the step in 2006.