Anywho, It was built in the late fifties for BT (still part of the GPO at the time), to house the central processor for the west of Scotland (probably just broke the DPA for tellin u' that), and is totally fortified!!
All the old engineers and operators used to talk of the tunnel in the basement (thats three basements down). The stories went that they were part of a network that were built leading to a bomb shelter under George Square.
There were underground Cold War telephone exchanges built in Manchester (known as Guardian), one in Brimingham (Anchor) and another in London (Kingsway.) These were built in the early 50's, and designed to withstand a Hiroshima sized (20kton) bomb over their cities. The idea was that even if the city was destroyed, the phone network would be maintained.
Anchor was the largest, completed in '57 at the cost of £4 million. Locals were told a new underground railway was being built, but the project halted for being uneconomic.
Advances in the size of Nukes made these structures obsolete by the time they were completed. They did however perform telecom functions, but are now mostly redundant.
Anchor is not even kept on a care and maintenence basis and is out of bounds to even BT staff for health and safety reasons.
Guardian is used as a secure cable route, meaning that city streets don't need dug up (interesting in light of one of the Glasgow comments)
Kingsway was offered for sale by BT in '96.
More on Anchor
When taken of the official secret list, reports at the time apparently mentioned a Glasgow exchange, but there's no evidence that it exists. Unless Hidden Glasgow readers know otherwise....