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
Wintry weather into the weekend
Jeremy Hunt could impose controversial new contracts for junior doctors by Monday, ITV News Political Editor Robert Peston has learned.
A new video has emerged online purporting to show a four-year-old British boy blowing up a car and killing three prisoners on behalf of IS.