I think going to a country as a backpacker and going to a country to look for a language institute/ homestay are two completely different things. If you are thinking of going to work on your english or whatever in that way, I would suggest arranging that sort of thing ahead of time. You can't really just show up with very limited funds and say "Hey, I'm here to learn your language, open your house up to me!" Right?
That said, I think its marvelous that you want to do that.
If you're truly backpacking, dont worry about a strict itinerary to tell the immigration people. They're used to backpackers. Although British Immigration is a royal pain in the ass.