I was of the mind that BT tells my previous Internet provider that I am leaving. Is this actually the case, or do I have to do all the legwork to manually shut everything down with my former provider? I am still getting billed by them.
if you use the openreach connection for your internet and take out a new contract with BT then BT should automatically advise your existing ISP that they are now taking over your phone line and becoming a BT customer
Bear in mind that if you have Openreach "fibre" broadband (FTTC), you will lose your existing connection, and if the cabinet is full, then you may end up with a basic broadband connection.