Interestingly the new password has updated on MyBT as well. I ONLY updated the email password and for one day I could still use my original password for MyBT! Now I have to use the new password for both sites.
The guy at BT said I shouldn't have the same password for both my emails and MyBT and that might be where the problem started. If that was the case then BT shouldn't have changed the password for MyBT. They shouldn't even be able to do that?!