Yes, they are a scam.
I get these so called BT calls at least a couple of times each week. When they rang last Friday I was snowed in, bored, unable to get out of my house, so I thought I would humour the caller. He asked, did I live on my own, how old was I, did I have a bank account. He then went on to ask details of my bank card, at which point I gave him an earful and put the phone down. To me, all they're interested in is clearing out your bank account.
The sad thing is, these con artists must find it profitable making all these calls or they wouldn't be doing it. If only one in a hundred, or even one in two or three hundred people, are taken in from one of these calls, then these crooks must consider they're having a good day. Shame on them.