Half of people are smoking less since the ban on smoking in enclosed public spaces in England took effect six weeks ago, a survey suggests.
It can take several attempts to quit successfully
A third of 1,000 smokers polled by Ciao Surveys said they now smoked less when out in bars and clubs and more than one in 10 said they smoked less altogether.
But only 1.8% said they had quit since the ban.
And a fifth said the ban had not made any difference to their smoking even though they wanted to quit.
The government hopes the ban, which began in England on 1st July, will help smokers to quit as well as protect people from the dangers of passive smoking and discourage children from taking up the habit.
A Department of Health spokeswoman said: "We estimate that a complete smoking ban might reduce smoking rates by 1.7%; taking smoking from 24% now, down to 22%.
"This will mean around 600,000 fewer smokers in the long term.
"However the primary aim of the legislation is to reduce the risk from exposure to second-hand smoke."
Doctors estimate second-hand smoke kills more than 600 people a year.
About 10 million UK adults - a quarter of the population - smoke cigarettes.
Polls suggest about 70% of smokers would like to quit.
Among the 1,000 questioned by Ciao, three in 10 smokers and nine in 10 non-smokers were in favour of the ban.
Nearly all non-smokers and two-thirds of smokers said bars and pubs were nicer places without smoking.
But 61% of smokers and 24.2% of non-smokers said pubs now smell of other odours such as sweat and stale beer.
Amanda Sandford of Action on Smoking and Health (ASH) said the survey findings were promising.
"It's very positive that half are saying they are smoking less. Every cigarette smoked causes harm.
"And we shouldn't be discouraged by the fact that less than 2% have quit smoking.
"We are expecting more and more to quit with time. Quitting smoking is not easy and it may take several attempts."
Forest (Freedom Organisation for the Right to Enjoy Smoking Tobacco) say the smoking ban is out of all proportion to the risk from second-hand smoke.
A spokesman said: "The statistics do sound very much in line with what happened in Ireland when they banned smoking in public places.
"Initially you see a small drop in consumption and smoking rates. But I suspect, as occurred in Ireland, over the next 12 to 18 months we will see the rates go back up to be very near to what they were before the ban."
The ban includes all pubs, clubs, membership clubs, cafes and restaurants.