In 2014 there were 128, compared with 165 the previous year and 207 in 2004.
Fewer women smoking and campaigns to teach new parents the safest sleeping position for their newborn - on their backs - are both factors, experts say.
The Office for National Statistics said the fall was driving the downward trend in overall unexplained infant deaths.
Figures gathered from the ONS include cot deaths (sudden infant death syndrome) as well as deaths of children younger than one for which the cause remained unknown even after a full investigation.
Together these accounted for 8% of all infant deaths occurring in England and Wales in 2014 - 1% lower than in 2013 - with just over half of the victims being boys.
Rosie Amery, from the ONS, said: "A number of factors may have contributed to the fall, including warmer than average temperatures throughout the year, fewer women smoking at the time of delivery and greater awareness of safer sleeping practices," she said.
The ONS began recording sudden infant deaths in 2004.
Overheating is a known risk factor for cot death and during cold winters the risk of the baby getting too hot under extra clothing and blankets is increased, according to experts.
There are measures people can take to lower the risk of sudden infant deaths and Francine Bates, from the Lullaby Trust charity, urged parents to follow the "safer" sleep advice - lying babies on their backs at bed and nap time.
- Always place your baby on their back to sleep
- Avoid smoking when pregnant or around the baby after it is born
- Place your baby in a separate cot or Moses basket in the same room as you for the first six months
- Use a good condition, firm, flat and waterproof mattress for your baby
- Never sleep on a sofa or in an armchair with your baby
- Don't sleep in the same bed as your baby if you smoke, drink or take drugs or are extremely tired
- Avoid letting your baby get too hot
- Don't cover your baby's face or head while they are sleeping or use loose bedding