If telnet results in a blank screen and a flashing cursor, it indicates a connection has been established and is waiting for input or output
Agreed, but then you would expect some response when you do type something even if erroneous. At least with the TBB one you do get some feedback when you type into it.
Anyway, this is all academic. BT email can be accessed from any network incl. PN. The OP just needed to get the email server settings correct & has now confirmed it works.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 20 Meg WBC