I'm from Europe. There's all kinds is new regulations around 2fa for banking apps that came out last year, logging in seems to absolutely require a phone now, and all my accounts use an app to do it.

Neither of my British accounts require a smartphone to log in, they send an SMS or make a voice call. My Danish account uses either an app or SMS.

You probably can't use a startup bank, as the app is one way they cut costs. Use a boring bank.

Just curious: Doesn't you Danish account still support the little cardboard card with the one-time codes?

Personally I really hate that they want to kill the card, and go to an app model (with the option of a key fob). It's made even worse by the police (and others) pushing the idea that the app is safer. How is it safer to have your two-factor authentication app on the same devices as the apps that need the second factor? Those things should be separate.

You are correct, I can also use the code card of one-use keys.

I was confused by the recent change where online purchases require an SMS or the app, and no longer work with the code card.

I think the app is probably encouraged since it protects against a phishing site like this: hxxp://tilbagebetaling1060dkk.net/1060DKK/ -- but I'm not quite sure how.

SMS as a 2nd factor is ( for a very good reason ) prohibited by dspp2 European directive. You.might have escaped that with brexit though. Even old school banks ( French dude here ) are forced to use apps as 2fa, but my bank for example can provide an hardware token, or a smartcard.

UK here:

Barclays don't require the app. You can still use the website or even telephone banking with a real agent. They do give you the chip and pin reader, the same as the one used in branches which works well.

Santander do seem to use a mobile for 2FA but only to send a text message and you can still use the website.

I rarely have to do more than 1 banking transaction / week so I just use the website, from home. Not too bothered about having another app, especially with access to my bank account.

In case you use macOS and own a M1 mac, check if your bank's 2fa app works on macOS. Your bank can deactivate it but iOS apps default to being runnable under macOS.

2fa through SMS? You don't need a smartphone for that.

I don't know about Ireland, but in Portugal most banks have a Web app and not just a mobile app.

Sorry I should have been clearer - the banking app is Monzo and they don’t have a web app for mobile or desktop

If you're using monzo I'm guessing UK - pretty much all the banks other than monzo, starling, revolut are _fine_