Health visitors and nurses may need to increase their education efforts as a poll reveals that the link between smoking and cot death is underestimated by 70% of UK parents.
The Foundation for the Study of Infant Deaths (FSID) polled parents two weeks after the UK public places smoking ban was put in place.
Most parents of with young children up to 3 years of age did not know that tobacco smoke might increase the likelihood of cot death.
A baby who regularly spends one hour a day in a smoky environment is twice as likely to die from cot death as a baby who lives in a smokefree home.
But 47% of parents living in the UK thought smoking conferred no risk or a much lower risk than is actually the case.
Low incomes families and those living in the north of England were more likely than wealthier families and those living in the south to underestimate the risks.
FSID-funded cot death research Peter Fleming from Bristol University said: "We all know about the danger that secondhand smoke poses to the public and yet we expose children to cigarette smoke in the home.
"Parents need to be aware of the threat that smoke poses to their children and protect them by enforcing their own smokefree zones at home."
FSID Director Joyce Epstein added: "Even if parents do smoke, they can have a really positive effect on reducing the risk of cot death by making their home a smokefree zone and always going outside to smoke."