Mr Voce was speaking after a report by Demos, the independent research institute, came out calling for children's play to be given a higher priority politically.
"There aren't many areas that are exclusively for children, but schools are one," he said. "What we would like to see schools doing is having a play provision in the grounds before and after school, staffed by qualified play workers - and not just for children who attend that school. It would be such a fantastic solution to what is becoming a serious problem - that children don't have anywhere to go to play."
Mrs Gerri Bennett, deputy head of Westborough Primary in Westcliff-on-Sea, Essex, said: "We opened up our playground for 17 years. Schools have a lot of public money going in and they should be public facilities. This year, for the first time, we've not been able to do it because older youths are causing trouble. Certainly we will reopen it, if we can."
The report, Seen and Heard, called for recognition that children's play is about more than designated playgrounds. It also called for a 20mph speed limit in residential streets.
Other recommendations included giving children an anti-social behaviour hotline to report adults who stop them playing, and creating iconic play spaces next to important tourist destinations.
Researchers Joost Beunderman, Celia Hannon and Peter Bradwell spoke to young people aged 6 to 18 in Bristol, Fleetwood, Sheffield, Maidstone, Bolton and Islington.
They found "children spoke about wanting to play football and to play outside. Rarely did they mention wanting more playgrounds as such."
Part of the problem with playgrounds was that small budgets and risk aversion led to areas with unexciting equipment, they said. Although better play spaces could be designed, the real challenge lay in making public space as a whole more child-friendly.
The report comes after the children's charity Unicef put Britain at the bottom of 21 nations in a league table of children's well-being and the Primary Review, led by Professor Robin Alexander, also flagged up concerns that children's lives were too pressured.
Tim Gill, former director of the Children's Play Council, has just published a book, No Fear, which also calls for children to be allowed to take risks.
"A community where children are out and about is a happy and healthy community, a community at ease with itself," he said.
Seen and Heard: Reclaiming the Public Realm with Children and Young People, www.demos.co.uk.