Two things I would say about Leaving Londinium.
One is if you know how to drive (I am not being sarcastic - cars not needed in cities, or whatever), then take some simple road trips up north. For safety in that regard: know how to change a tire, keep the gas tank filled up (when you get between a half and a quarter tank stop at the next station), and use maps, not just GPS. If you have a good sense of direction, great and if not, then work on it. Lots of quaint towns and places to walk without going out into the wilderness alone. Kew Gardens is even on the train route, but maybe you have already been there.
Second it possible to hike (or horse trek!) with groups. And before you say "but I hate people" (LOL ; )) just bear in mind that this is a way to get out in nature without having to worry about who or what is behind or in front of you. Chances are if you are quiet, other hikers would respect that and maybe some would even be cool. ;) I remember one time you said rock climbers annoyed you and I had to laugh because I was in that community for a while in college and they are kind of like quants actually. I enjoyed the time with them, but wasn't going to make climbing my life. Sailing on the other hand...
Anyway, perhaps this seems simplistic, but I understand what you mean. It's not a safe world out there and female hikers do have to be careful. Still, there are solutions.