Parents worry more about their children being murdered than much more widespread health problems such as obesity, a survey suggests.
The findings, in a YouGov poll of 1,244 parents, contrast with data showing the risk of a child being killed by a stranger is a million to one.
The risk of severe health problems for children due to lack of exercise is one in three, figures have suggested.
The latest figures show walk-to-school rates have fallen to a new low of 48%.
The survey for charities Parentline Plus and Living Streets is being published as part of a campaign to get more children walking to school.
Both charities argue that parents can increase activity levels using measures such as walking to school instead of using a car.
Of the parents polled by YouGov for the charities, 30% said they most feared that their child would be abducted or killed by a stranger, while a further 30% feared they would be hurt in a road traffic accident.
But only one in 20 picked concerns about poor health in later life due to the child's levels of physical activity.
The chief executive of Parentline Plus, Jeremy Todd, said stranger danger and road traffic accidents were real concerns to some parents of primary school children who chose to drive their children to school.
The parenting counsellor for the charity, Valerie Outram, said she could understand why parents perceived the risks in this way.
"Even if you presented statistics that said it's not really very likely that this would happen, there's always a little part of you that says my child might be that one in a million and I just don't want to be taking that risk," she said.
All time low
It was also about the long-term nature of the risk, she added.
"Just because a child is a bit podgy doesn't mean they are going to die early, but if they get morbidly obese - it's a different matter," she added.
The chief executive of Living Streets, Tony Armstrong, said the number of children walking to school had dropped to an all-time low.
The latest figures, which are for 2008, suggest 48% of primary age children walk to school.
"It's certainly not wrong for parents to fear road accidents or abduction, but it is wrong that fear for children's health is put on the back burner, especially when the statistics show that there is more chance that their children will suffer long-term health problems from obesity," said Mr Armstrong.
The poll also suggested many parents underestimate how much exercise their children need.
The government recommends they do at least seven hours of physical activity a week.
According to the research, 68% of boys and 76% of girls are not meeting that recommendation.