Greetings
I agree that Virgin is the best way to go if you want to stop in the Lake District. Otherwise, GNER has been advertising fares as low as £10-12 for Edinburgh to London.
Flying (only if you are skipping the Lake District) can be cheap, but like the train, you have to buy well in advance to get the cheapest fares. Also, you should take into account the time it will take to get to/from the airport and through security. Might be faster on the train. Also there are no weight limits for luggage on the train and you don't have to worry about the one carry-on item limit.
BMI is good, but I would avoid British Airways if at all possible. And Heathrow - it's a nightmare for luggage and for just about everything else. You can get cheap flights on EasyJet or FlyGlobespan etc. into other airports.
Kate