NHS recommendations are for all youngsters aged six months to five years to be given daily vitamin drops, but parents have to pay for them unless they are part of the free Healthy Start programme.
Evidence suggests take-up of the vitamins is low among poorer families but even children in better-off families may not be not getting enough.
The Nice review comes as Professor Davies published a report on children's health, detailing the need to invest in young people.
It said reducing obesity by one percentage point in children could save the NHS £1 billion a year due to fewer long-term health problems.
More top news
Danish submarine inventor Peter Madsen has been sentenced to life in prison for torturing and murdering Swedish reporter Kim Wall.
A BBC chief said reporters also had a responsibility to be sensitive in their broadcasts.
Layla, a 7 and a half year old black rhino, has undergone what’s believed to be the first computerised tomography scan on the species.