The Foundation for the Study of Infant Deaths (FSID) has carried out a "secret shopper" survey of the marketing of baby products in stores in England, Wales and Northern Ireland.
It found:
Precautions
Babies should sleep on their backs
Keep your baby's head uncovered
They should sleep with their feet at the foot of their cot
They should be tucked in to stop them wriggling
They shouldn't get too hot
They shouldn't be exposed to smoking
Bedding which covers a baby's head poses a risk of cot death.
The researchers also found that independent shops were more likely to undermine the 'reduce the risk of cot death' message than chain stores.
Shops in the North of England were the most likely culprits.
Every opportunity
Joyce Epstein, FSID director said: "Cot death claims the life of a baby every day in the UK and lifesaving advice needs to be offered at every opportunity.
"We are very disappointed to see so many baby shops undermine the safe sleep message.
"Shops must do better, particularly smaller shops and shops in the North."
Dr Angela McLoughlin, a lecturer in health visiting and FSID trustee said shops' failure to provide advice was confusing parents.
"Manufacturers and retailers need to be responsible and learn that there's more to think about than matching nursery equipment if we are to give babies the chance of a lifetime.
"Clear advice about safer sleeping is all we are asking of manufacturers and retailers of baby products.
"This is not complicated advice but it could just save a baby's life."