Sounds really exciting Exo!
My first piece of advice is to keep your backpack as small as possible - it´s so difficult to hump them around on a crowded train, and trust me, in England all the trains are crowded!
You might want to check out "student" rail passes for UK and Europe; they used to do special monthly deals for people under 25.
Also, if you don´t mind a rather boy-scouts atmosphere with curfew, strictly no booze, and dormitories for sleeping, you can investigate these guys for a network of cheap, well-placed accomodation:-
https://www.yha.org.uk/membership