Yes, you can take alcohol onto trains on the whole but not onto Transport for London services and you'll probably find most train stations and even some services will be covered by drink-free orders from local councils.
Also, I'll tell your right now, everyone hates you. I hate you, your fellow passengers hate you, the guard hates you, anyone that sees you will hate you. There is nothing worse than stupid teenagers drinking and being loud on a long-distance train journey. Don't be surprised if some big geordie man doesn't come over and punch you in the eye.