I used to wander all over the woods around that area when I lived in Kent, very rarely saw anyone or indeed much wildlife except in specific areas. With all the things that have been released there not sure how much wandering around I would do now, even if the larger animals don’t pose much of a risk the change to habitat and increase in ticks and mosquitos and associated diseases might.
[perhaps I am provoking discussion to say that]
I used to wonder on the chalk hills above Cosham - I think they allowed cattle to graze there - much like the 'controlled fires; at the Cape.
Loved the spot, with panoramic views of the sea, quite a lot of flowers - photographed my first UK orchid there.