In benign weather conditions, properly equipped and on non-extreme terrain, there isn't much to worry about. You're just going for an extended walk. It's not like you're climbing K2 or trekking through the Amazon rainforest, hiding from bandits. Even trying hard, it's not easy to find places in the UK where you won't bump into people, especially in England and Wales - believe me, I've tried.
Obviously it's a different matter it you try Ben Nevis wearing jeans and trainers in the midst of a snowstorm.
Just get on and do it. Pick a location you can get to, get a map/GPS and plan a circular walk and do it. I quite often only have a rough plan and wing it as I walk depending on what I see in front of me. I personally don't fear it at all so maybe not the right person to give advice on that but really, the chances of anything bad happening are pretty small and you can just as easily meet a sticky end in urban areas. To be honest, if I died on a hill I'd count that as a pretty decent end compared to what I hear most people going through in the "safety" of hospital beds.
Start off with a day walk and when you're hiking, look around for spots that you could camp. You'll see scores of them and you'll soon realise there is nothing to it.
It really is not a big deal.