Earlier quoted context omitted.
Around here every bank require 2fa for logon and then again for signing payments (although you can queue and batch sign a number at a time. )
Barclays in the UK does 2fa if you order it, otherwise this strange bit with just parts of the password. They also have the most complicated 2fa I've seen. You get a pocket-calculator-like device where you need to insert your card (chip and pin type), then you enter your personal code, and then you do a challenge-response thing where you enter a code generated from the website into the device, and it responds with a…
Such a thing is rather common in The Netherlands, though it's often not a second factor but just the way you log in to online banking. It avoids having you remember yet another password, instead you just use the same card and PIN you need "offline".
Side note: At the end of 2014 Rabobank (one of the banks with such a system) replaced those devices (which they called "random readers") with "Rabo scanners", which have a built-in camera to automatically read an image from the website instead of having you manually enter a code.