Online parenting forums should also carry nutrition advice, Demos said, after a survey found that many mothers are "in the dark" about healthy eating for toddlers.
More than half of 1800 mothers surveyed said they were confused by contradictory information provided to them by health professionals and on food packages.
Many were also unsure about portion sizes for their children and vitamin supplements.
Louise Bazalgette, author of the report, said: "This research shows that important public health messages about children's nutrition just aren't reaching enough parents.
"It paints a worrying picture of mums who are anxious about a lack of advice and also conflicting advice when it comes to feeding their baby or toddler healthily. We spoke to some parents who were confused about whether they should trust what they read on a food packet, or what their health visitor said."
Separate research, conducted by Vitabiotics Wellkid Baby Drops, found that by the age of three, six in 10 children crave sugary snacks.