In reply to Tom Ripley Mountain Guide:
Another vote for the Oly TG series. I have the TG3, and like others have mentioned, it has been used and abused in most environments - trad, alpine, sport, underwater, winter conditions, used on school expeditions and generally thrown around. It has survived all of that and still looks new!! The shots are amazing and every time I go out, I just pop it into a small black zip up soft case with a 240 cm sling through it, put it over my head and shoulder, and that's it. I see a good picture, I draw it like a gun from a holster.
If you want other recommendations - Oly TG4; Panasonic Lumix; Oly OM-D E-M5 Mark ii; Oly OM-D E-M1
I know you mentioned budgets. I went to the camera store to buy something that was worth 80 quid and walked out with a TG3 for 280. It looked incredible and I was not disappointed. If you can afford any Olympus camera, or a Panasonic Lumix, you won't go far wrong.
Enjoy the photography
H.