Throughput will depend on many variables, including how many users are using the 'pipe' from the exchange onwards (this is known as 'contention ratio'), the connection which the server (computer) which hosts (stores) the website uses and your upload speed (the speed your computer can talk to the exchange) and download speed (exchange to your computer).

The speed you have been quoted is the download speed. The upload speed will be a lot less (typically 390kbps, 1.3Mbps or 2.5Mbps). This is what the 'A' in ADSL stands for (Asynchronous). The reason for this is that when you download a page / video / software from the internet, your computer simply says "can I have a bit of this file" and "next" while the computer at the other end sends you the various chunks of data.

Depending on the website I am connected to, I get throughput of 2Mbps-12Mbps (roughly 0.2MBps-1.2MBps; b=bits, B=bytes)

BT may simply have downgraded the throughput to reduce customer expectations. This is also why they claim "Upto 20Mbps" rather than the actual "Upto 24Mbps" - you almost have to live in the exchange to get 24Mbps. (similarly for 40Mbps -v- 100Mbps for Infinity)