Four out of five people want the legal smoking age to be raised from 16 to 18 to prevent young people taking up the habit.
ICM conducted a nationwide phone poll on behalf of the BBC of 1010 adults in England, Wales and Scotland.
The majority of people surveyed thought raising the age at which teenagers could buy cigarettes would deter them from taking up the habit.
A slight majority thought the age limit should be raised to 21.
Of those questioned, 93 per cent supported increasing penalties for selling tobacco to children, and two-thirds said parents who allow under-age children to smoke should face prosecution, wrote Scotsman.
A quarter of people want the government to ban smokers being treated by the NHS for smoking-related illness, according to a BBC poll.
Some 27% said the government should discourage smoking by introducing the ban while 71% opposed the move.
The survey also found the public wanted to see the legal smoking age raised.
Just over half also thought smoking should be made more expensive, and three-quarters said there should be more spent on anti-smoking publicity campaigns.
The government is currently considering whether smoking should be restricted in the workplace, including pubs and clubs.
Its decision will be revealed in a Public Health White Paper, due to be published this autumn.
In the BBC survey, carried out between 20 and 22 August, two thirds of those questioned were in favour of such a ban, reports BBC News.
Read earlier news stories by PRAVDA.Ru