Hmmm - would BT email you to say that you had been blocked, then ask you for password information by email?
No. It's a scam.
Phone BT and report it - if you can stand their queuing system.
To check if your computer has been fiddled with you need to run an antivirus scan, and then any other useful programs you may have installed such as spybot and c-cleaner.
Find your antivirus program - it might be Norton, Macafee, Avast etc click on it and find 'run scan'. When the scan has run you might see it asks should it delete the following....hopefully it might say 'no threats detected'.