Emergency talks are being held over the future of children’s adventure playgrounds amid concerns that funding cuts are making some popular sites too dangerous to insure.

Anne Longfield, England’s children’s commissioner, and Sadiq Khan, the London mayor, have raised concerns after some playgrounds were told by a leading insurer that they were now considered too high-risk.

“Too many children are living a ‘battery hen’ existence, spending more and more time sitting in front of screens and less time outside playing. I want to see more playgrounds across the country, not fewer,” said Longfield, who has championed play as a weapon against child obesity and poor mental health.

“The government and local authorities should step in and work together with the insurers so that these vitally important spaces for childhood activity, creativity and adventure can be protected.”

‘I want to see more playgrounds across the country, not fewer’: Anne Longfield, England children’s commissioner. Photograph: Rex

Insurance industry sources said that signs of deterioration in some parks were forcing them to reconsider whether cover could be offered. Zurich insurance had previously informed three parks their policies were unlikely to be renewed.

Zurich underwriters told Glamis playground in Shadwell, east London that the company’s “appetite [had] changed towards adventure playgrounds”. Hornimans adventure playground in Kensington and Chelsea, west London, and the Felix Road playground in Easton, Bristol, have had similar notices.

Insurers have now agreed to meet the charity Play England to discuss how the threat to adventure playgrounds can be minimised.

Khan has written to Zurich, raising concerns about “the possible removal of insurance cover from some adventure playgrounds and the wider implications that this could have across London’s neighbourhoods and communities”.

Zurich said it was not withdrawing from insuring all play parks and would reconsider only those facilities it believed posed too high a risk.

“We are not saying no to insuring adventure parks – and we continue to insure most of the ones we’ve been working with,” it said. “Child safety has to be the priority here and we think the risks in just three of those parks are too great, so until those risks are managed and reduced by the parks’ operators, we won’t provide liability insurance for them.”

Campaigners said they were not aware of any increase in claims from adventure playgrounds, which usually are owned either by local authorities or charities. Paul Hocker, the director of the London Play charity, said: there had been “no groundswell of accidents”.

“If you go to an adventure playground, you will see lot of red faces. The children are moving all the time, they are creating games and being imaginative – and identifying and managing risk.”

Councils warned that general funding for such facilities was already stretched. Gerald Vernon-Jackson, chair of the Local Government Association’s culture, tourism and sport board, said: “Councils want to do everything they can to keep playgrounds and other spaces open and available to their communities in the face of unprecedented funding pressures but are now having to think of new ways of maintaining local services, including for playgrounds.”