[ItsBob]

I can tell you with almost 100% certainty: no banks in the UK use any 2FA other than SMS-based.

I spent December last year looking for a new bank to move to. One of my criteria (not the most important but it was on the list) was better-than-SMS 2FA.

No one offers it. There may be some niche, loosely-based finance org that does but none of the banks or Building Societies do.

So, unfortunately, you need it in the UK.

[iam-TJ]

Barclays, with standard current accounts, provides several methods none of which are SMS. There's a separate pin-code device (called Pinsentry) that does TOTP and challenge-response, or passcodes for both telephone and Internet banking.

[ItsBob]

Yeah, Nationwide has the little PIN code device which definitely helps with transactions but not logging in: that's still old-school.

[lrvick]

Most VoIP services support SMS. Still no cell phone hardware required.