ainsworth74 has this exactly right.
The legal system is an unknown thing for many people and it can be very hard to navigate or even understand on your first encounter. It's sometimes no clearer when you've been involved for a long time. I'll explain below the sequence of events that caused the matter to come to a head and maybe help some people in the future.
What has happened in this case is that the TOC has requested a summons to be issued in the Magistrates Court for the fare evasion. That has been sent to the address given at the time the offence was committed. The TOC no doubt tried to engage before the summons but got no reply as it all went to an old address. The date of the hearing came around and as there was no defendant* the case was proved in the absence of the defendant. A fine based on assumed income and costs would have been imposed. The notice would have been sent, again, to the incorrect address.
Unsurprisingly, the fine was not paid and the enforcement process kicks in. By now people begin to get interested in the defendant and try to track them down. With a name and a date of birth, it becomes possible. You may ask why no attempt was made to ensure that the right address was in the system and it's a good question to which I do not have an answer. Armed with this information, the "defendant" is summoned back to court to explain why the fine has not been paid. The court is not interested in the original offence at this stage, as far as it is concerned it is dealing with a convicted person who has defaulted on the financial penalty. They will be rolling up their sleeves to start threatening prison if the cash is not forthcoming.
It's around now that the defendant becomes aware that they have been convicted in their absence when the summons whacks on the doormat or a court bailiff comes calling. Here we have the remedy for the situation - that is to make a formal statement under oath that they were not aware of the original trial. This can be done at court, though it is easier and less risky to complete at a solicitors. This is the Statutory Declaration or SD and the fees are limited - I think £5 + a little more if you want a copy.
Here's the important piece which many people have repeated: You normally only have 21 days to make the declaration from the time you found out about the court case. Unless you have special, extenuating circumstances, and "I didn't think it was important" is not good enough, you must make that declaration. No declaration and the conviction stands!
Why less risky? An SD forces the whole process back to the very beginning, as if the summons has just been requested, with no court date yet set for an appearance. Courts are under pressure to close cases quickly, so if you appear in court and make the declaration they may well attempt to reopen the matter there and then and ask for a plea. You want to be prepared before you go to court and may want additional time to speak to the TOC. Going down the solicitor route gives you this time. Also, courts are becoming rarer than hen's teeth, so travelling to one is an issue for many people. When you have your SD, and a copy for yourself, send it to the court Signed For and hang onto the receipt. Call the court to make sure that have it and will be actioning it.
When a court receives your SD, they will inform the TOC and set a date for a new first hearing. They should also cancel the fines hearing. It's a good idea to make sure this has been done - the court service has been slashed to the bone and things can, and do, get missed. You don't want a bench warrant without bail to be issued.
A quick word about courts: If you are unlucky enough not to reach a sensible agreement with the TOC before the new court date, you will have to appear to plead not guilty. The court will not be ready to hold a trial on the day. First appearances deal with guilty pleas there and then if they can, trials are put off to many weeks later when they have more time set aside, so you will need to come back at a later date if the TOC will not accept your case that you were out of the country. Dealing with cases on the day is cheap - which is why courts give a discount for early guilty pleas on the day and a reduction in costs.
If it does go to trial, you may want to get some legal help - the way that evidence is gathered, presented and accepted can be technical and you would not want to fall foul of process and the law. What seems common sense to many people does not always apply in a court, though the rules will be there for a good reason.
*Of course, there was no defendant as they didn't know about the case. However, many people do choose to bury their heads in the sand and not show up. Some willfully refuse to attend and eventually, warrants will be issued for their arrest. The courts are not surprised that people don't show. Even more so for rail matters as they might have been caught in Manchester off a Virgin train, but live in London. The case would be listed in Manchester.