Are we living in the same world? Visa+MC are a duopoly borderlining being a de facto cartel organization and handle the vast majority of all retail transactions in the world.
The margins are extreme, but so are the barriers to entry. To build a new card network you somehow need to convince a bunch of banks and merchants to support your card network. Good luck with that.
The EU even forced Mastercard to allow others to start a card network running over their infrastructure, after they bought EuroPay. But it’s so hard to get people to actually use a new card network, that no ones actually bothered to try.
Also, I think it's important to remember but most of us don't go and select Mastercard or Visa, most of us don't care. We just use what the banks use. I suspect changing from Mastercard to Visa would be extremely expensive and it's a lot easier and more profitable to just pass along that to the customer.
You got the consumer part wrong. The consumer is the merchant, which can decide if they allow Mastercard cards or not. Same as many merchants don't accept Amex. It's because they don't like to pay the Amex fee. Same as many merchants don't accept Apple Pay or Android Pay or why some merchants only allow card payments for purchases of a minimum amount.
Merchants are the consumers and they decide what cards they will accept. Based on what cards they will accept consumers will be picky about which cards they want to have. For those exact reasons I have a VISA credit card as well as an AMEX because I sometimes can't use my AMEX, otherwise I wouldn't even have a VISA CC.
Also Apple Pay and Android Pay don’t cost merchants more to implement or use (assuming they have the HW, which any card reader from the past 10 years will have). The card network rules also forbid merchants from not accepting them, but of course rules don’t mean much without enforcement.
Finally there is really only one company that can undercut Mastercard, and that’s Visa. It’s only a question of time before Visa bump their fees, there’s no way they’re gonna leave money on the table for long.
Is it also legal to charge customers a fee based on what type of card they use? A large number of customers have multiple cards anyway, so that would be a meaningful incentive.
It is more likely there are significant regulatory or other burdens taking UK orders for EU goods.