TinselAngel, as long as you don't mind a bunk bed in dorm YHA is a very reasonable option for accommodation, especially if you're a member (£15 a year) More expensive on a Saturday night but £27 for Central London is not bad.
Can't really suggest cheap travel options though, all the rail discount stuff is for two people, and even then is not cheap #RipOffBritain
National Express can work out a lot cheaper but it seems to me to be more awkward to get to their locations (nearest train 7 miles away nearest NE pick-up 25 miles for me) and they are so much slower.