In reply to dking02:
I got into the outdoors while I was a cadet at school, the Cadet Centre for Adventurous Training provided really good instruction for very very little (and my travel was covered by Rail Warrants), you're young enough to get involved with the ACF/ ATC/ SCC and get the best out of it before you turn 19, some counties/ units will be better than others at getting outdoors and doing stuff (either the green stuff with weapons or AT).
Scouts are again good, Kent county has the Invictus Mountaineering Club which I believe accepts young people who are keen.
You may be able to find a local D of E group, given that you are posting on here you're probably interested in something a bit more out there than what the Bronze award would offer you but you could meet people who are keen to do more adventurous stuff.
People can probably come up with some suggestions of where to go and the best way of travelling by public transport, if you try the public transport option on google maps directions (make sure to change the travel time to when you intend to travel) you will get surprisingly good info on public transport options.