New tobacco legislation will ban the open display of products
The proportion of smokers who say they would like to give up smoking has fallen in recent years, figures from the Office of National Statistics show.
In addition just over half of smokers said they had made a serious effort to quit in the past five years, a figure lower than in previous UK surveys.
But the poll did find the numbers who say they would not smoke in front of a child has increased in the last decade.
There now appears widespread awareness that smoking can cause harm to others.
At 67%, the percentage of smokers who said they would like to give up smoking when asked in 2008/2009 was "significantly lower" than the 74% recorded in 2007, the ONS reported, although it is in keeping with findings prior to that year.
The ban on smoking in public places introduced in England and Wales in 2007 - and in Scotland in 2006 - is seen as one key reason many more people may have expressed a desire to quit that year.
But prices have risen in the meantime, and efforts to persuade the population to give up have continued.
Targets for reducing the prevalence of cigarette smoking have been set out by the government in the Smoking Kills White Paper, the Public Health White Paper and the Cancer Plan.
The proportion of people smoking has in fact remained fairly constant in recent years, comprising just under a quarter of the adult population.
The number of cigarettes smoked is down from the mid-1990s, but has remained static since 2004: just over a quarter of smokers make their way through a packet or more a day.
In the last decade, the number of people who say they would not smoke in front of a child has increased dramatically - from 54% in 1997 to 77% in this latest poll.
Across non-smokers and smokers, there was generally significantly more support for the smoking ban in restaurants than pubs.
Only 6% of smokers said they wanted to give up because of the ban on lighting up in public places, which was introduced in England in mid-2007, and slightly earlier in Scotland and Wales.
The vast majority of would-be quitters said they were motivated by health reasons. Nearly a third said they wanted to give up because they could not afford it or considered it a waste of money.
A packet of 20 cigarettes now cost nearly £6.
Dr Jennifer Mindell from the Faculty of Public Health said the drop in the numbers wanting to quit showed 2007 was "basically a blip".
"It's more or less what we would have expected. The smoking ban was a good trigger for some people but many people quickly realised they could carry on smoking.
"The picture is a mixed one. There is progress being made, but the more investment we put into anti-smoking measures the better. It is money well spent and it will save us in the long-term by reducing the serious illness smoking causes."
Betty McBride, policy & communications director at the British Heart Foundation said: "Stopping people from ever becoming addicted has to be a priority.
"It is still too easy for children to evade age restrictions on purchasing tobacco by using cigarette vending machines. A full ban on vending machines is the only guaranteed way stop children using them and protect them an addiction which threatens their future health."
A Department of Health spokesman said: "Smoking is at a historic low, thanks to individual efforts and Government action such as Smokefree and raising the age of sale.
"This survey shows continuing high numbers of smokers who want to quit, and high levels of support for Government action to help them - and to protect children.
"We are currently taking legislation through Parliament to prohibit the display of cigarettes, with the aim of reducing the number of children and young people who take up smoking and helping smokers wanting to quit."