This seems like a massive jump to conclusions.
I have had a lot of banks and credit cards, mobile payment apps like Venmo/PayPal in the US and they almost all work on mobile web and desktops.
But I recognize that wealthy western countries didn’t really skip the personal computer like many mobile-first regions have done.
It’s not like the UK sent out a mandate to private banks or any other private industry on this issue. It’s also only one small country of hundreds.
I’d have to question this idea that this is how things “already look.” I can think of very few businesses that I interact with that force me to use an app.
I’d like to know what private businesses are copying the kind of workflows and customer experience you get at the USPS or DMV.