Hi,
I seem to remember there was some earlier discussion on this: probably through notes. I know I did a bit of sleuthing and was unable to come up with anything other than it was a disused sports facility. The statement that it is a LNR is of course incorrect because this is a statutory designation. “Nature Reserve” itself can be used by anyone without any implications as to a status in law (there are numerous private nature reserves & many reserves run by the Wildlife Trusts have no statutory protections). It may be worth seeing if it has been designated as an LWS, although these have little or no protection other than being noted in planning applications.
The situation is not that different from Hounslow Heath Golf Course (still labelled as such, but re-tagged as landuse=grass), which also needs a bit of attention. Such former sports sites are not uncommon (there’s a big disused golf course to W of Leicester & a private school playing field near me has been unmanaged since around 2010-11.
Probably this is the best approach, possibly with the addition of "former " to the name. alt_name may be suitable for the “…nature reserve” if it is indeed referred to by this name locally. Clearly it doesn’t really have a name at present, but people will know it as Warren Farm in one way or another, so another alternative is just to truncate it to Warren Farm.