Also credit card companies must be getting a fair bit if Santander can afford to give you 3% cashback for buying train tickets using its 123 credit card, albeit with a £24 annual fee.
Fees are charged by the acquiring bank/institution to the merchant for every transaction. The acquiring bank is not the bank which issued your card though (i.e. when a Santander customer pays for a train ticket or some groceries, there's no fee that gets pocketed by Santander) but rather the bank which processes the transaction on behalf of the merchant.
These acquirer fees are a larger percentage for low-value transactions, and a smaller percentage for higher-value transactions. This is the reason some third-party shops which provide recharges for the Metrocard system in Adelaide will refuse to accept credit card payment for recharges of less than $20, because the commission provided to them by Adelaide Metro is not enough to cover the cost of processing the transaction.
As for the Santander promotion, that would be all about taking a small loss leader and using it to hopefully make a whole lot more money off you from interest and fees in the long run. The only way that a consumer can "win" from a rebate scheme like that where xx% is offered on certain types of sales is if they pay off the credit card bill in full every month (i.e. not incurring interest) and they use the rebates enough to offset the fees they pay for accessing the scheme.
Maybe fares could be reduced if there is just one ticket selling website and an extra fee for using a credit card instead of a debit card.
You're almost onto it!
Very large businesses can become acquiring institutions in their own right, so that they only have to pay the real costs of that administrative work instead of paying a fee to some other acquiring bank/institution which includes a profit margin every time they make a sale.
For something as large as the UK rail system, the volume of CC transactions would easily be enough that ATOC could set themselves up as an acquiring institution. From that point on, every TOC would use ATOC as their CC acquirer, paying a single yearly contribution towards that function of ATOC instead of a fee for every single transaction going to a for-profit bank. The effect on the TOCs would be that increasing the proportion of CC transactions (as opposed to debit cards or cash purchases) would actually make things even cheaper for them, all without the need to cut down on the number of sales channels or resorting to the old hat non-solution of imposing punitive fees on CC use.