This mid C18 map fragment shows the area Honor Oak (Oak of Arrnon) some 150 years after Queen E's honourable and elderly frolicking.
   

The map suggests that only the wooded area is honor oak, and it is a large area, covering most of the square roughly bounded by Wood Vale in the West, a prototype Honor Oak Pk (Rd) in the North, Brockley Rise in the East and London Rd/Stanstead Rd to the South.

More precisely, it looks like a strip of land east of Wood Vale was cleared of trees, so if you are West of Tewsbury/Netherby then you probably are not in Honor Oak nor if you live on Sydenham Common ie South of Westwood Pk/Ewelme Rd.
So perhaps Honor Oak Rd, when built, cut right through the area designated as Honor Oak! Which is reasonable.

It is reasonable to think the wooded parcel of land north of Honor Oak Pk (Rd) is also Honor Oak.

With so many old trees in this area then, I wonder if much later on, the one tree left standing on One tree hill was designated the symbolic focus for our historical wishful thinking?
And so the actual oak tree that was present at the 'royal resting' might still be alive in someone's garden in the above described areas.

PS Also, you'll notice Forest Hill does not exist on this map - it is just an administrative area after all. Perry Vale Ward is well established at the bottom of the image of course.