I have just added this to the map of places to fly your drone at Drone Scene:
https://dronescene.co.uk/where-to-fly-drone/beckenham-place-park/london/1825
Land owner permission requirements unknown.
Not sure on the permission here, I check through the website and searched 'drone', couldn't find any mention of it. But I went at sunrise (5:40 ish) so only the odd jogger / dog walker about. Nice place to fly, lots of trees, but also open space to the Mansion, and a lake. Did have a crash, but nevermind, it's all good practice, and it's 60/40 the drone's fault… lol.
The originator declared that this location was not inside a Flight Restriction Zone at the time of being flown on 09/05/2022. It remains the responsibility of any pilot to check for any changes before flying at the same location.