Good evening,
I also have to agree with Nell and Groom over ScouseBoys claim. I would also query all the assumptions made that it has to be some form of institution. Just because it has a couple of benches in the garden.
I have 2 benches in my garden but that doesn't make it an institution or school or hotel.
Windblown trees doesn't have to make it a coastal location. Just anywhere on higher ground with stronger prevailing winds and no apparent higher ground behind.
Location wise I don't think it's South Downs. Whilst I can't claim to know every square inch of them, I think a remote clump of Scots pines would stand out in my memory. Certainly not along the top at least. It is though in my opinion rural and perhaps alone.
The Weald, including Ashdown Forest, the Vale of Sussex, Vale of Kent, Surrey Hills are all good contestants for the location. But could also be North Hampshire, Berkshire, Oxfordshire, Hertfordshire, Buckinghamshire to name a few.
Why would someone have a house built, I still believe this is one house and always has been although extended and altered, with an observation tower? It doesn't look like your typical farmhouse so not to look over their prize cattle or whatever.
But what about the racehorse owner/trainer? somewhere to watch out over the gallops. Have checked out parts of the Lambourne area (West Berks).
Maybe just a particularly good view over spectacular countryside.
Because we can't find it on-line doesn't mean it's been demolished, just that we havn't come across it yet or nobody has ever put pictures of it up on-line yet.
If you look at a great many big houses or mansions the "Front Door" is where the drive is. But the "Front" of the house looks out over the gardens or parkland. So I think we are looking at the front of the house and the front door is on the other side as is the approach to the house from the road. Having two or more doors doesn't make it more than one house, just that they wanted to be able to access the gardens from different parts of the house. The one on the left from a main reception room and the other from the main hallway.
Enough of my rambling, just some thoughts but don't give up till the fat lady sings as they say.
John915