Cycling was the biggest issue raised at the Royal Parks' "meet the managers" day last week.
The event, held in Hyde Park, aimed to let the public find out more about how parks are run and have more of a say.
Royal Parks chief executive Mark Camley said more authorities should run open days to get feedback on their parks.
Camley said: "People have been complimentary about the policing of our parks. There have been two big issues raised - dog walkers' concerns about dangerous cyclists and cyclists wanting more cycle routes in parks."
Camlley added Royal Parks would only sanction routes with high safety levels, which they check with WS Atkins Consultants.
A new Royal Parks Considerate Cycling campaign means cyclists not on cycle paths in parks can get an instant £40-£60 fixed penalty fine. Dog fouling and littering also attract the fine. The Royal Parks previously did not have the same powers as councils to charge fines.