Eventually they did suggest I call the number on the back of my card, but I was annoyed by their lack of professionalism by this point (I mean, they are asking me to do stuff - giving out information to unknown callers - which they themselves always tell customers never to do!) I said I wasn't going to phone a general number and get stuck on hold for hours over an unknown issue - either give me some reference to get through quickly to the right person, tell me what the problem is now, or send me a letter. But they kept claiming that they couldn't send out letters in the post :-(
In the end, I finally received a letter by mail telling me that there were problems with my direct debit payments. So it was a genuine call but their inability to securely make these calls is frustrating.