Had one last week and knew exactly what it was. Played along, with them.
Acted a little "dumb" - so whn asked to open windows I said why, the weather is cold and raining. So he told me "no, your computer". The a few more stupid answers and comments. Maybe 10 or 15 minutes and finally he got to the:
Press "Win & R", what can you see &c then type "http:// ... .com" into the box (which I did not) and enter. Kept him hanging on whilst it connected (a little slow) then siad "Yes, it has come up with a new screeen" and he asked what it said to which I responded "Be careful, some ****er is trying to scam you". CLICK and he was gone.
At least it stopped someone else getting a call.
And I can see how someone might get caught out. I have some major issues at present and spoeaking with BT frequently. Someone without background knowledge that is having issues could easily fall into the trap ...
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M H C
taurus excreta cerebrum vincit