I wonder whether the upper half of the Triangle could be fenced off as a dog exercise area, with the lower half as a dog-free play area for kids. Then the sloping field in the Horniman Gardens could ban unleashed dogs (with leashed dogs still allowed) to make a nicer area for kids and sunbathers.
"The Horniman Museum is a charitable company, limited by guarantee. It is also a Non-Departmental Public Body of the Department for Culture, Media and Sport (DCMS). This means that although it receives most of its funding in the form of Grant in Aid from DCMS, it operates at "arms length" from central government."