Extracted some information and pushed for more. The dangerous part of this is that the caller was able to say "look at the phone number written on the back of your Barclaycard" - and, indeed, it is the same number ("or if abroad +44 1604 269 900").
BE CAREFUL! Guy on the phone said he was calling from Barclays Fraud Prevention team investigating number of suspicious transactions on my account. Asking for card details, recent transactions, etc.