. . . . The question being asked was if the TOC could then insist that the passenger use a different payment method to the one they intended (card) with the potential force/compulsion being in the form of laws against ticketless travel.
We still cannot reach the point where 'force' or 'compulsion' is introduced. There is no 'forcing' the passenger or 'compelling' the passenger to do anything (other than the Byelaw provision of removing a person from the Railways if necessary, but these would be in different circumstances).
To answer the new part of your question, can a Railway Operator insist that a passenger uses a different payment method, then I still claim that the wrong word is being used. There is no insistence - it is for the passenger to pay their fare if they choose to travel, and only if they choose to travel, the negotiation over the transaction (which includes payment) should be just that, a negotiated settlement. The remedy for an non-paying passenger may, indeed, be a prosecution just as it may be an invoice for the fare due - that distinction would be made on a balanced view of all the evidence.
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To DaveNewcastle and Clip in particular:
If I am only carrying cash, which is an accepted payment method on Northern Rail services, do you think that walking past a card-only TVM would constitute "failing to pay"?
If the full circumstances are that both parties (the passenger and the Railway Operator) have developed the custom and practice of paying for rail travel by cash on the journey in question, then it would be hard to see how that could be construed as "failing to pay with intent to avoid payment".
It is a matter of fact (following from the way in which the question is constructed) that the passenger has "failed to pay". I hope that much is clear to all.
The real difficulty arises in interpreting a passenger's intentions when they have 1) chosen to travel, 2) failed to pay, 3) posess the means to pay, 4) have passed an opportunity to pay. At first blush, these 4 conditions might lead an inquiring mind to find evidence of intention to avoid payment. Futher investigation might reveal other factors which make that conclusion less probable.