The lake district is nice, but I believe scotland, ireland and even wales are nicer.
Places to avoid are all industrial cities, such as manchester, birmingham, liverpool, etc.
Remember: you may not sleep over in york.
There are flights with CO, leaving from lots of airports, such as EDI, DUB, GLA, etc.
Train for some reason is called a luxury transportation method, so by bus (they call it coach), its much cheaper.
Even better is renting a car. Unless you have prolonged stays at places.