Smoking is the cause of major health problems
Ministers dropped legislation to ban advertising from this year's programme, a move that angered anti-smoking campaigners.
The poll, conducted on behalf of Action on Smoking and Health (ASH), also suggests that many people continue to believe that lobbying by the industry and influential figures such as Formula One's Bernie Ecclestone may be to blame.
There was outrage in Labour's first term of office when it was revealed that the party had received a £1m donation from Mr Ecclestone.
This was followed by a long-lasting exemption in proposed tobacco sponsorship rules for Formula 1.
The donation was later returned by the party, which denied that the cash had influenced the decision.
Ban supported
Sixty-three per cent of people polled by ICM Research on behalf of ASH said they supported a ban on tobacco advertising.
Professor Gordon McVie, director general of the Cancer Research Campaign, said: "It's hardly surprising the public is so cynical.
"Health professionals, the general public and even the government have stated that they are opposed to tobacco advertising. Only the tobacco industry is in favour of it."
At the Imperial Cancer Research Fund, director general Sir Paul Nurse said: "It's clear that banning tobacco advertising would be popular move."
John Connolly, of ASH, added: "A private members bill to ban tobacco advertising will be debated in the autumn.
"The government should back this or introduce its own Bill immediately Parliament returns."
The government is to spend millions over the next few years encouraging smokers to quit , through advertisements, funding of drugs that make it easier to quit, and helplines.