In reply to LMR:
If you're properly new to hillwalking then starting out with a two day walk carrying all your kit in October is a pretty full on way to start! Most people would probably start off by stopping at a campsite and doing a couple of one day walks - that way, you get some idea of how fast you walk before you commit to a multi-day route, and also figure out how to do camping efficiently (ie work out what you do need and what you don't need) in a situation where you aren't carrying all your kit and have the option of hiding in the car if it all goes tits-up for whatever reason.
That out of the way, the basic places you're going to be looking at are Dartmoor, the Scottish Highlands, North Wales or the Lake District. Camping out on the hills is officially allowed in Dartmoor and Scotland and unofficially tolerated provided you do it responsibly in North Wales and the Lakes. There's loads of great routes to be done, although if you're new to it then you'll probably want to pick stuff that's relatively easy and not too committing (ie something where it wouldn't be too hard to escape to civilization if you had to) until you've got more of an idea of what you (and your gear) can handle.
