ADSLGuide reports on a piece from The Scotsman newspaper, which states that a BT telephone exchange on the island of Foula has been enabled for ADSL broadband, albeit only at 512Kbps:

The 35 BT customers on Foula, 15 miles west of Shetland, have finally been linked to the high-speed internet service, nearly a year after hurricane-force winds demolished a partly constructed building for the new equipment.

Completion of the work on Foula means its exchange is the last of 1,069 in Scotland to be upgraded for broadband. It is also the last of 378 to be covered by a Scottish Executive broadband initiative for rural and remote areas.

However, several other islands, including Iona, and Flotta and Graemsay in Orkney, have yet to be connected because they are located too far from the nearest exchange.

So not technically the final exchange, but getting closer.