Can't resist the opportunity for a bit of history...

During and immediately after the war the triangle was a smallholding, with chickens and geese. There was a cottage at the top, near the Sydenham Rise/Sydenham Hill corner.

The Dulwich Estates Governors are the freeholders of the triangle and after WWII they leased it to the LCC as an extension of Horniman Gardens. In 1954 the LCC created "a children's play area with sandpit and paddling pond".

The LCC (who at the time also managed the Horniman Museum and Gardens) designed the triangle with particular attention to the needs of children. The paddling pool and the sand-pit (near the site of the cottage) were built, and the spoil from these was used to create a series of banks and pits that children could climb over and hide behind. These banks are still apparent. The refreshment kiosk and lavatories were also build at this time, and there was a notice at the entrance banning adults unless they were accompanied by a child.
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On the abolition of the GLC responsibility for the park passed to Lewisham Council, but the Estates Governors remain the freeholders. This fact alone, I imagine, makes it highly unlikely that there will be a change of use.

And there is not one shred of evidence to support the suggestion that it was once a plague pit.