The footpaths inside the park need to be marked with bicycle=no as per https://www.royalparks.org.uk/visit/parks/green-park/faqs

"Cycling is only permitted along the roads which surround the main park. These include Constitution Hill (which is part of TfL's C3 cycleway and links up with St. James's Park and Hyde Park). Smaller paths across the park where cycling is not allowed have clear 'no cycling' signage at ground level. Please be considerate and give space to other park users and the park's wildlife. Pedestrians have priority at all times."