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 Prime Minister will detail her 12-point plan on negotiating Britain's exit from the European Union during a speech on Tuesday.
Police investigating the disappearance of Victoria Cherry, who was last seen in October 2015, have found a body.
Unpaid internships should be banned to prevent young people missing out on jobs in top professions, a new report has said.