This comes despite admissions from parents that the average age they played out alone as children was seven and a half years old and some were as young as five years old.
Stranger-danger and abduction was cited as the biggest concern, with almost 50 per cent saying it is their top fear, according to the poll from www.familiesonline.co.uk.
This was closely followed by worries about child safety crossing roads, which concerned 41 per cent of parents.
The fear of abduction and stranger-danger was also greater in parents with girls, whereas parents with boys were more likely to worry about road safety.
Faye Mingo, marketing director at Families, said: “The question of when is too young to play out alone is a continued debate amongst parents today and for good reason.
“We all remember playing out alone from a much younger age as children ourselves and it seemed a completely ordinary thing to do, but years later, we find ourselves as parents in the connected world of 2017 and we are certainly much more aware of the risks on our doorstep.
“The question is, when do we let go?
“We want to instil independence and confidence in our children, but we want to keep them safe, too.”
The findings also showed increased anxiety for parents in rural areas in comparison to more urban locations in relation to exposure to strangers – yet the study revealed parents who live in rural areas are more likely to allow their child to play outside alone from a younger age.
Marguerite Hunter Blair, chief executive of Play Scotland, pointed to a recent study that showed that high school children often have the road safety skills of five-year-olds in the 1970s.
She said: “However, we are being overprotective. The underlying problem is that parents are undermining the competence of their children, which means that they roam less far than they would have done in the past.”
Edinburgh Council last week launched a trial scheme to help parents close streets to traffic for their children to play outside over the summer months. Families can close a road for play up to five times between April and August, free of charge.
Ms Hunter Blair said that parents were turning to organised events and activities such as the Girl Guides to provide “risky but supervised” experiences for their children that they otherwise may have had for themselves.
She said: “The Girl Guides have a huge waiting list as parents want children to enjoy outdoor ‘risky’ experiences such as building a fire, but under supervision.
“You can understand where the fears come from, but how do we break it?”
Other concerns cited by parents about letting children out alone were fears about bullies, where their offspring were going to play, who they are with and whether what they are doing will get them into trouble.
The poll also found that traditional games such as tag and hopscotch were top of a list of activities enjoyed by modern youngsters when playing outside.