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
The UN has said it is deeply concerned by reports hundreds of Syrian men have disappeared amid a mass exodus from rebel-held areas.
A man suspected of planning a terrorist attack has been arrested in Rotterdam after police found a loaded AK-47 in his apartment.
Another mild day with highs reaching up to 13C degrees in mild southerly winds