My son picked up a £20 fine last week.
I presume, from your title, you mean a Penalty Fare. A Penalty Fare is not just another word for a fine, it is something quite different. It's a civil charge that, in certain circumstances, a train company is permitted to make. A fine would only result after being prosecuted and convicted in Court, and this is much less serious (at this point) than a fine.
I'm not going to waste a lot of time trying to appeal
It's far from a waste of time - many appeals are successful and we may be able to provide advice for a successful appeal here too, depending on the circumstances. It's not just about the money, either - if you have previously been issued with a Penalty Fare then this is held on record; if you ever enter into a dispute again with a train company then they may see this and treat it more seriously than they otherwise would have done (e.g. jumping straight to prosecution). It's certainly worth considering, and I'd be grateful if you could provide the details of the circumstances (train company, what happened, which stations and so on).
The whole setup seems unprofessional, like some sort of scam outfit.
Numerous operators operate Penalty Fares schemes in an unprofessional, non-Regulations-compliant and potentially unlawful manner. It's no surprise, then, that the payment portals are no better.
I could send a cheque but worry that it 'might not arrive'
If you sent a cheque through the appropriate means (e.g. Signed For post) there could be no suggestion it hadn't arrived in time.
we'll be in for further payments or a summons.
Additional amounts, such as "administration fees", sometimes demanded on top of a normal Penalty Fare are not enforceable in any way; there is no statutory or contractual basis for them. Penalty Fares can indeed be cancelled for non-payment, resulting in potentially more serious outcomes, but it is possible to appeal a Penalty Fare without paying it in the first instance. Appeals are generally handled fairly quickly nowadays, so if an appeal is considered and upheld within 21 days of the issuance of the Penalty Fare, it might never be necessary to pay the Penalty Fare at all.
Also of important note is the fact that, if you submit an appeal against a Penalty Fare and the appeal is responded to by the appeals body, or the 21 days which they have to do so pass without a response, and the Penalty Fare has not been cancelled or withdrawn in the intervening period, the train company is
statute barred from prosecuting any relevant offence in relation to the incident. This is a very valuable protection which itself makes it worthwhile to appeal the Penalty Fare if you are in any doubt as to its validity.
I have seen that you mentioned that the Penalty Fare was issued by West Midlands Trains. Their Penalty Fares scheme is not, in my experience, compliant with the Regulations, on a number of grounds including the lack of signage at all, or compliant signage, at a number of stations. Accordingly, Penalty Fares issued by them may well be successfully appealed against.