I don't think you ever spoke to BT, and you didn't speak to McAfee either.I tried to install my McAfee virus protect from my BT link, it wouldn't work, I rang BT tech dept and instead of talking to their tech dept I was directed straight to a customer service advisor at McAfee. He said he had to take control of my machine and said I needed software for a year on top of the free intro 30 day McAfee software on the new machine.
The key to answering how you got scammed is to pin down where exactly that fake BT link was. How and why did you have a "BT Link", or where was it you got the phone number from to call "BT Technical Department"? I don't think BT even has a Technical Department! Do you have the web page address where that link or phone number was?
It is worth you getting to understand this as next time you go to your BT Link they will do something else bad to you.