However there is strong support for new laws to make tobacco advertising less attractive to children.
The survey showed that only 20% of the 427 adults surveyed in the East of England knew that there are 100,000 deaths as a result of smoking every year in the UK.
Cancer Research UK says the survey result backs up its ongoing campaign to remove all attractive and stylish designs from tobacco.
It says glossy packaging adds to the allure of cigarettes. Standardized packaging would remove this and increase the impact of picture health warnings.
The campaign says smoking causes more than eight out of 10 cases of lung cancer, and starting smoking at a young age greatly increases the risk of lung cancer.