If I have understood you correctly, in the past you have been asked on two occasions to pay penalty fares (and have done so). Yesterday, you were pulled over and not offered a penalty fare but instead told that the railway would write to you. I am assuming that all of these incidents involved Southeastern.
The normal course of events is that Southeastern's letter will say that they are considering prosecuting you, and ask if there is anything that you want to tell them.
@Hadders has some excellent advice on how you should respond to this letter: you can see the advice
here. But in this case, it's hard to know what the outcome will be. If Southeastern know that you have twice previously paid penalty fares, they may think that however much you promise to pay the right fare in future, you don't mean it: they may decide that taking you to court is the right thing to do.
If you are taken to court, then you will be charged under either the Regulation of Railways Act ('RoRA'), which means that Southeastern think that you meant not to pay the right fare, or under the railway byelaws, which is just a factual question of whether you had a valid ticket or not. This will mean that you have to go to court, or if you are prepared to plead guilty everything may be dealt with by a 'single justice procedure notice' which deals with everything by post.
If you are convicted, either of these charges will result in a fine, plus compensation (the train fare that you didn't pay) plus court costs, plus the prosecution's costs. Expect the fine to be around half a week's income, and everything else to amount to maybe £500 (could be more, could be less). A RoRA conviction in particular will have to be declared for the following year for things like getting insurance or starting a new job. There are some jobs (typically those involving handling money or a lot of personal trust so things like nursing, medicine, personal care and so on) where you will always have to declare a conviction - even one under the byelaws - for the rest of your life.
I don't think it's our role here to make moral judgements, but I think it's fair to point out that the chances of the railway taking you to court increases with every time you come to their attention. As this is the third time, you will be lucky if you do not end up being prosecuted. Being caught on future occasions will lead to further chances of being prosecuted and fined: ultimately repeated RoRA convictions can lead to time in prison. The easy way to avoid this happening is to pay the proper train fare every time you use a train.