Almost nine out of ten mothers who lose a baby to cot death smoked while pregnant, say researchers.
The risk increased if the baby was exposed once born
The Bristol University team said the risk also increased with every hour babies were exposed to passive smoke after birth.
The number of cot deaths has fallen, but those linked to smoking have risen.
The report, to be published in the journal Early Human Development, suggests public smoking bans will make people more likely to smoke at home.
Many other studies have shown a clear link between smoking and cot death, but the Bristol research tries to unravel more precisely the cost of smoking both before and after birth.
Smoking among pregnant women has fallen from 30% to 20% in the last 15 years.
The experts found that the proportion of babies who went on to die from Sudden Infant Death Syndrome (SIDS) who were born to mothers who smoked during pregnancy had risen from 57% to 86%.
This, they say, is mostly due to the success of campaigns to lay babies on their backs to sleep, which is credited with preventing hundreds of cot deaths.
The remaining cot deaths are now much more likely to be due to smoking.
The report, from the university's Institute of Child Life and Health, said that fresh messages about the dangers of smoking while pregnant had to be given to women.
Lead author Professor Peter Fleming said: "What we have been trying to do is look at the whole impact of exposure, both before and after birth, to smoking and its adverse effects.
"After delivery, the mother can reduce the risk by protecting her baby and not smoking near it."
Hour by hour
He found that for every hour a newborn was exposed to tobacco smoke, the risk increased.
"We found a perfectly linear relationship," said Professor Fleming.
"The risk of death increased with each individual hour the baby was exposed to smoke.
"For example a baby exposed to smoke eight hours a day was eight times more likely to die from SIDS than a baby that was never exposed. These are startling statistics."
He said that although the recent introduction of smoking bans in public buildings led to a "potential increase" in smoking at home, the findings might send an "encouraging" message.
"What it is saying to parents as a positive message is 'even if you can't give up smoking, don't smoke around the baby'."
Professor George Haycock, from the Foundation for the Study of Infant Deaths said: "The figures show that maternal smoking is now the most important avoidable risk factor for Sudden Infant Death Syndrome (SIDS).
"If no women smoked in pregnancy, about 60% of cot deaths could be avoided. This means that in the UK the number of deaths could fall from around 300 a year to 120 a year."