I know that you can get an Apex fare if you travel in advance, but is there a website where you can book cheap rail travel in advance, or with certain conditions? Thanks!
GNER operate east coast mainline services, for example, London to Aberdeen. If that is not in your travel plans, have a look at this site. http://www.thetrainline.com/default.asp?target ='_blank' href=http%3A%2F%2Fwww%2Egoogle%2Eco%2Euk%2Fsearch%3Fhl%3Den%26q%3Dtrainline%26btnG%3DGoogle%2BSearch%26meta%3D&T2ID=2166_200788235221
Beware of independent sites, such as Trainline. I used to run a railway station and I've seen plenty of tickets issued by these firms which aren't valid for travel. (e.g. tickets sold under a promotion offered by company A for travel on the services of company B, which doesn't accept the tickets).
The National Rail website shows all available ticket prices, together with links for online booking: http://www.nationalrail.co.uk/