I suspect that many of the so called Blackheath Society would not be remotely interested in the realities of the daily life on the heath unless there is a monetary gain for them. Many houses and places on the heath have been used for filming and television productions, giving the owners money so there is their incentive. Suggesting that an almost 100 year old enterprise, looking after the locals and travelers needs for refreshment without the society having a percentage would be useless because the snobs wouldn't be seen to be slumming it with the likes of the public on "their" heath !
The Tea Hut is as integral to the area as much as anything else. It obviously doesn't stop the local heath maintenance contractors using the facility so why stop anyone else by restricting parking?

I was a regular visitor to the HUT in 1998/9 and the year of the eclipse.
It was a place to go that wasn't McDonalds, Animal Burger was egg-tastic.
I have so many good memories of working at the old golf club building at the top of the
hill that burned out so many wagon clutches!!! The smell…
After a night out walking across in the dark to devour a bacon butty.
Nice time of my life.

I live in Blackheath. Just watched Tea Time. The Blackheath Society guy is an utter douchebag.