how come BT Internet users cannot access their emails from the BT Internet website?
Why should they? There is no hard and fast rule that an ISP must only provide its email itself.
I show you another strange arrangement. AOL BB users have their email, and their user IDs, provided by a diff company, AOL UK a subsidiary of AOL Inc USA, and have always have done. This is cuz when CPW (TT) bought AOL Inc's BB some years ago they did not include the email and user IDs. AOL BB and AOL UK are diff firms as can be shown from their websites:
AOL BB:
http://www.aolbroadband.co.uk/ (Like BT, you can't access your emails from here)
AOL UK:
http://www.aol.co.uk/ (You access your emails from here)
You may consider it an anomaly that whilst BTw provides Orange's BB, it is not involved in their email. Orange still provides its own email and its email servers, I believe, are hosted in France by France Telecom.
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 19 Meg WBC