nationalrail.co.uk describes itself as the 'definitive source' for rail travel information. On
this page it lists all the acceptable payment methods. Since, for instance, someone wanting to pay with a certain payment method (say, Amex) but who is unsure if this is accepted might Google 'national rail payment methods' and see this as a first result, stating that:
Thus, any reasonable person in that situation, having read the above statement, would be influenced in their buying decision such that they might believe they are able to pay either at the station, or on board if they cannot buy their ticket at the station due to the facilities not accepting their valid payment method.
Thus, by virtue of
Section 50(1) of the Consumer Rights Act 2015, the validity of Amex as a payment method is a binding contractual term. If Northern decline to accept Amex then this is not the passenger's problem.
There can be no question that Amex is not as widely accepted as Visa and MasterCard, or that Amex generally charges higher fees to merchants. However, it is unquestionably valid as a payment method on trains that are part of the National Rail network, and so any problems with acceptance are those of the train company and not of the passenger.