Their security practices for online banking are pathetic in comparison to HSBC. HSBC gave me a one time key dongle which breeds more confidence than the various articles about santander's lax security I've read.
The caller would say "I'm calling from First Direct" and then get confused when I asked for proof of this.
You get called by a computer that asks you to identify yourself by picking a piece of personal information from a list. It might ask for the month and date of your birth, for example, and give you 5 options.
Because there are 365 possible month + date combinations, and yours appears in the list, you know they already have this information so you're safe to confirm it, and they also get to confirm that you are (likely) who they're intending to talk to.