Or have they switched to using mobile phones for authorisation?

I only need it to set up new payees.

Yeah new payees and direct debits etc. and any changes to them.

Still using the card reader – but you only need it for a few things (new payees mainly).

They have a phone app which can do some useful things (like getting cash out from an ATM without a card) but it doesn’t do payee authorisation via the app.

If your payee is already set up, either via the card reader or by a payment you’ve asked In branch for them to make, you can use the phone app without limits. I do this every month from my business account so I can pay myself a salary, dividend, expenses etc
You can also set up a new payee but with a £250 limit. Any more and you need the card reader

like getting cash out from an ATM without a card

Awesome. I hope other banks are going to add this!

I think they also do Apple Pay through the app, but my iPhone 4S is too old for that. 🙁

Yes, they do

Oh and they also do Paym which lets you receive payments to your telephone number.