Why? Is it to flag you as "stupid" on the account. I mean, if I was a bank, and called a customer asking personal details over the phone from an anonymous number, and they gave it, then I would make note.
After all, any fraud later would be "We have on record that you are quite happy to give personal details regarding your Barclays account to anonymous callers on the phone, so we have to assume you broke the terms of your account (again) and gave details to a fraudster - no refunds".
Is it some con?
Or just a stupidity test?
Oh, second trick was for him to give me a number to call him on !!! LOL
Turned out to be real, i.e. from Barclays, having called back on known numbers. Took 6 minutes and about as many call transfers to get to the bottom of it though.