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On some parts of the railway, there is a 'penalty fare' system, which can mean that you're given a docket requiring you to pay your usual fare plus £50 (rising to £100 if you take more than 14 days to pay). But this system isn't universal, and even where it exists the railway can choose not to use it.
In this case, I suspect that the railway's officer has chosen not to use this process. So what will probably happen is that at some point you will get a letter from the railway. This may arrive in a few days, or it could take up to about six months. That letter will most probably be headed something like 'Notice of intended prosecution' but don't panic: if you read it closely you will find that while the railway might take you to prosecution, at this point what they want is your side of the story.
At that point, we generally suggest that you should reply courteously, and apologise for your mistake.
@Hadders may well be along shortly with a very good description of what your letter should say, but you should make it clear that you will make sure that you always pay the right fare in future. And you should offer to pay the fare that you should have paid, plus the cost of the railway's investigation (which is likely to be somewhere between £100 and £200).
As (in my view) the main thing that the railway wants to get out of the process is reassurance that people will not systematically dodge their fare again, it will be pretty likely that they will agree to settle out of court, as long as they think that you have learnt your lesson. If they are prepared to settle like that, then pay the settlement, and the matter's over - you won't have to go to court and you won't have a criminal record.