Whilst this forum is mostly about Perivale Park, there are many other fantastic green spaces in London to explore. One of my favourites is the nature reserve in Tower Hamlets in east London, the cemetery park.
This place has a remarkable history which is still visible, and a wide diversity of nature. The signs in the park are always informative and often highly original. There is a communal compost where you can take away a bag or so for your own garden, an apiary, many different flower meadows and lots of activities for visitors organised by a very active friends group. The following photos derive from only a partial exploration of the area; there is much much more to discover than shown here. The reserve also has wonderful seasonal variation, it is worth going there at almost any time of year.
And to end, a very unique aspect of the park located in the Ackroyd drive green links area; the remarkable railway viaduct art and murals.