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
Urban Outfitters has apologised for a 'red-stained' sweater bearing the logo of a US university where four students were shot dead in 1970.
Edinburgh's poet laureate has offered some words of reconciliation as Scotland prepares to vote on independence in just two days' time.
Temperatures will be on the rise in the next few days, with highs of 25C in the sunshine by Thursday, but do not expect clear blue skies.