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
A cat who survived a brutal beating because he looks like Hitler has battled back from the brink of death to make a full recovery.
A father-of-three was killed in a car crash on the same day he was given the all clear from cancer.
Conservative MP Guy Opperman has caused a stir by claiming Liverpool striker Mario Balotelli was in the House of Commons for a drugs debate