I had a similar issue in Ealing - the bylaws forbid cycling in parks, yet more recent literature from the council encourages it. I spoke to a park ranger who said that they don't enforce rules against cycling in parks unless combined with anti social behaviour. I felt highway=footpath, bicycle=permissive, segregated=no was the best representation of reality where there was no signage explicitly forbidding cycling.
https://www.openstreetmap.org/way/23135636#map=16/51.5084/-0.3094&layers=YN