Metafilter, what is the best day hike in the British countryside, accessible by public transport from London?
I've been in London for the past few weeks, and in the few moments that I've had free from work, I've seen pretty much all of the major tourist attractions, quite a few smaller museums/random things and have eaten quite a few amazing meals (Joel Robuchon=win).
I've got one last full Saturday before I fly out on Sunday mid-day, and am trying to figure out what is the best use of my time. Right now I'd like to do a hike or long walk somewhere outside where it is properly green/muddy/not a park/slightly more wild.
I haven't seen much of the British countryside, and have been toying with the idea of visiting Stonehenge, visiting the sea, or somehow getting to the Vale of the White Horse to see the chalk horse. However I am constricted to public transport, and don't know
what is the best use of my last day in the UK. I don't mind traveling 2-3 hours to get there, but would like to have a destination worth it.
I have a fairly generous budget to get where I need to go, but am not willing to rent a car and drive on the wrong side of the road.
Metafilter, what is the best day trip/hike in the British countryside?
(and yes I've see this question and it is making lean away from stonehenge and the white horse as both of those are probably best seen from air/not very fun to visit/not worth the trouble. Also I'm not really attracted to castles/mansions/estates.)