If you are considering travelling fro Norwich to London and you don't want to spend a lot of money the first thing you should do is to book your ticket in advance.
If you book your train or coach ticket a few weeks or even one month before the day you want to travel prices are much cheaper.
You can check and compare the fares online:

-By Rail: www.nationalexpresseastanglia.com/

-By Coach:
www.nationalexpress.com/

Don't forget to check the fares with Megabus, they are usually very cheap!: uk.megabus.com/