I suspect the amount has come from taking the last year's price of an Anytime Single from Totnes to York, route "not via London", which would have been £179.90, and then adding on administration costs of £80.00. The latter figure is a commonly used figure for such settlements.
Unfortunately, whilst the cost of £259.90 is very steep, I would suggest paying it in this case, provided his Railcard was indeed out of date, as your son would be liable for the cost of the undiscounted Anytime Single one way or another: he did actually travel, and he didn't have a valid Railcard, so they are entitled to recover that fare. The administration costs of £80.00 are not cheap but I would suggest it is likely that any other resolution of the matter is going to cost more.
The only possible saving grace I can suggest is this - on which date in October did this occur, and by which date are they asking for the settlement to be paid?
You don't have to tell us the exact dates, but if the latter date is more than 6 months after the former, they will be out of time to bring a prosecution. That is because, for Magistrates' Court offences such as these, there is a strict time limit of 6 months from the date of the alleged offence for the prosecutor to lay an information before the Court (i.e. start the prosecution process). I suspect they will be in time, but only just.