The poll of 1,002 people was commissioned by Play England to launch its Manifesto for Children's Play. The body is calling for a range of measures, including 20mph zones where children live, protection of school playtimes and more supervised play services after school and in the holidays.
The manifesto asks all political parties to adopt three pledges - to make all residential neighbourhoods child-friendly places where children can play outside, to give all children the time and opportunity to play throughout childhood and to give all children somewhere to play in freedom and safety after school and in the holidays.
Play England director Adrian Voce said: "Our research shows that children's play is a serious issue for voters. Parents know that safe neighbourhoods with attractive places to play near their homes are vital to their family's quality of life and to their children's health and development."
He added: "Our research shows that adults clearly think there is a big role for the Government in making this a reality."