I had a reply from the email I sent to the Brockman family, but unfortunately it didn't really help. The reply I recieved was:

Dave I know nothing abut Stone Wood but I will refer you to one of my relatives in the UK who might be able to shed some light on this. His name is Hugh Drake-Brockman. If Hugh can help, I’ll give him your email and ask him to contact you direct. All the best Alan

However, I have done some firther research. I found a PDF, which I will upload when I've finished reading it, that gives a guide of how to research a wood. When it came to finding out the owner of the wood, they suggested starting with the Tithe maps, which were used in the 19th Century to calculate how much tax people had to pay. With this being the case the maps needed to be accurate in both name and area and it's also an official document.

By looking at these maps that I found online, https://www.old-maps.co.uk/#/Map/621500/136500/12/100762 it initally showed Little Stone Wood in existence in 1873 (this I knew already) but on another website http://www.kentarchaeology.org.uk/Research/Maps/Maps%20intro.htm

they were able to confirm that Rev William Brockman owned Stone wood. The reason why this has been so hard to find is because in some documents LSW is refered to as Stone wood and in other Little Stone Wood. What also blurred the issue is that the area of land he owned was split in two by a boundary and so some was recorded under Folkestone and the rest under Saltwood. Also in the email I recieved bak, Alan Borckman refers to LSW as Stone Wood. The only doubt left remaining is that in one ledger there is a reference to Stone wood and Little wood, which again confuses the matter, but I think it is now safe to assume that LSW was owned by the Brockman-Drake family and then sold to the army in 1970, who are the current owners. This could also explain why it looks to be untouched for a number of years as the army would not manage the wood, they are more interested in running around with guns pretending to shoot people...

Below are screenshots of the research I conducted to discover the owner of LSW

I also think I could of found out why LSW has managed to exist since the 1600s. My latest theory is that the wood used to be coppiced and so provided wood for the local community, probably beachwood park. This is because the trees in the forest have a distinctive look where they have a wide base with a lot of small trunks coming up. On my next visit I will get a leaf sample and then identify the tress, but this theory does seem to be the most likely.