SInce IdahoBackwoods posted as well, I'm inspired to recommend Idaho to everyone in Britain.
In my mind, Idaho is one of the undiscovered gems in the US, in terms of sheer beauty, it's up there with Montana and Wyoming, although nothing touches Alaska on that score.
However, the difference is that even in the US, most people don't explore Idaho and there is more wild adventure there than you can believe.
Sometimes I think there's almost a secret club of US outdoorsmen who know about Idaho. It's just not on lots of people's mental maps -- but oh god the country there is fabulous...
Plus in lots of spots it's great place for wildlife watching. (If I remember correctly, it's done a lot of wolf re-population -- that's something I have yet to see, wild wolves in the lower 48... Alaska and the Yukon territory, yes, lower 48, no....)
Anyhow, if you love the wilds, check out Idaho, you won't be sorry.