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
Sir Gerald Kaufman Labour MP for Manchester Gorton and Father of The House of Commons has died aged 86, a family spokesman said.
A very unsettled start to the new week with heavy, thundery, occasionally wintry showers spreading in from the west throughout the day.
It had been reported that four domain names which appeared to support Clive Lewis for Labour leader were registered in June last year.